QoS Scheduler/Shaper for optical coarse packet switching IP-over-WDM networks

(1)

QoS Scheduler/Shaper for Optical Coarse Packet

Switching IP-Over-WDM Networks

Maria C. Yuang, Po-Lung Tien, Julin Shih, and Alice Chen

Abstract—For IP-over-WDM networks, optical coarse packet

switching (OCPS) has been proposed to circumvent optical packet switching limitations by using in-band-controlled per-burst switching and advocating traffic control enforcement to achieve high bandwidth utilization and quality-of-service (QoS). In this paper, we first introduce the OCPS paradigm. Significantly, we present a QoS-enhanced traffic control scheme exerted during packet aggregation at ingress nodes, aiming at providing delay and loss class differentiations for OCPS networks. Serving a dual purpose, the scheme is called ( )-Scheduler/Shaper, where and are the maximum burst size and burst assembly time, respectively. To provide delay class differentiation, for IP packet flows designated with delay-associated weights,( )-Scheduler performs packet scheduling and assembly into bursts based on their weights and a virtual window of size . The guaranteed delay bound for each delay class is quantified via the formal specification of a stepwise service curve. To provide loss class differentiation, ( )-Shaper facilitates traffic shaping with larger burst sizes assigned to higher loss priority classes. To examine the shaping effect on loss performance, we analytically derive the departure process of ( )-Shaper. The aggregate packet arrivals are modeled as a two-state Markov modulated Bernoulli process (MMBP) with batch arrivals. Analytical results delineate that ( )-Shaper yields substantial reduction, pro-portional to the burst size, in the coefficient of variation of the burst interdeparture time. Furthermore, we conduct extensive simulations on a 24-node ARPANET network to draw packet loss comparisons between OCPS and just-enough-time (JET)-based OBS. Simulation results demonstrate that, through burst size adjustment, ( )-Shaper effectively achieves differentiation of loss classes. Essentially, compared to JET-based OBS using out-of-band control and offset-time-based QoS strategy, OCPS is shown to achieve invariably superior packet loss probability for a high-priority class, facilitating better differentiation of loss traffic classes.

Index Terms—Departure process, IP-over-WDM networks,

Markov modulated Bernoulli process (MMBP), optical burst switching (OBS), optical packet switching (OPS), quality-of-ser-vice (QoS), traffic scheduling, traffic shaping.

Manuscript received August 11, 2003; revised February 3, 2004. This work was supported in part by the Phase-II Program for Promoting Academic Excel-lence of Universities, Taiwan, under Contract NSC93-2752-E009-004-PAE, in part by the NCTU/CCL Joint Research Center, and in part by the National Sci-ence Council (NSC), Taiwan, under Grant NSC93-2213-E-009-049.

M. C. Yuang, P.-L. Tien, and J. Shih are with the Department of Computer Science and Information Engineering, National Chiao Tung University, Hsinchu 300, Taiwan, R.O.C.

A. Chen is with the Optical Communications and Networking Technologies Department, Computer and Communications Research Labs, Industrial Tech-nology Research Institute (ITRI), Hsinchu 310, Taiwan, R.O.C.

Digital Object Identifier 10.1109/JSAC.2004.833837

I. INTRODUCTION

T

HE ever-growing demand for Internet bandwidth and recent advances in optical wavelength-division-multi-plexing (WDM) technologies [1] brings about fundamental changes in the design and implementation of the next generation IP-over-WDM networks or optical Internet. Current applica-tions of WDM mostly follow the optical circuit switching (OCS) paradigm by making relatively static utilization of individual WDM channels. Optical packet switching (OPS) technologies [2]–[5], on the other hand, enable fine-grained on-demand channel allocation and have been envisioned as an ultimate solution for data-centric optical Internet. Nevertheless, OPS currently faces some technological limitations, such as the lack of optical signal processing and optical buffer technolo-gies, and large switching overhead. In light of this, while some work [4], [6], [7] directly confronts the OPS limitations, others attempt to tackle the problem by exploiting different switching paradigms, in which optical burst switching (OBS) [8]–[14] has received the most attention.

OBS [8] was originally designed to efficiently support all-optical bufferless [9], [10] networks while circumventing OPS limitations. By adopting per-burst switching, OBS requires IP packets to be first assembled into bursts at ingress nodes. The most common packet assembly schemes are based on timer [15], packet-count threshold [10], and a combination of both [10], [13], [16]. Essentially, major focuses in OBS have been on one-way out-of-band wavelength allocation (e.g., just-in-time (JIT) [11], and just-enough-time (JET) [9], [12]), and the sup-port of QoS for networks without buffers [9], [10] or with lim-ited fiber-delay-line (FDL)-based buffers [14]. Particularly in the JET-based OBS scheme that is considered most effective, a control packet for each burst payload is first transmitted out-of-band, allowing each switch to perform JIT configuration before the burst arrives. Accordingly, a wavelength is reserved only for the duration of the burst. Without waiting for a positive acknowl-edgment from the destination node, the burst payload follows its control packet immediately after a predetermined offset time, which is path (hop-count) dependent and theoretically desig-nated as the sum of intranodal processing delays.

In the context of supporting QoS in bufferless OBS networks, the work in [9] employs a prioritized extra offset-time method. In the method, a high loss priority class is given a larger extra offset time, allowing the high-priority class to make earlier wavelength reservation than lower priority classes. The method effectively provides different grades of loss performance, but at the expense of a drastic increase in the end-to-end delay particularly for high-priority classes. Besides, as discussed in 0733-8716/04$20.00 © 2004 IEEE

(2)

YUANG et al.: QoS SCHEDULER/SHAPER FOR OPTICAL COARSE PACKET SWITCHING IP-OVER-WDM NETWORKS 1767

[17], the method undergoes the unfairness and near-far prob-lems. Especially due to the near-far problem, a low-priority burst with a longer path to travel may end up with the same or larger offset time than that of a high-priority burst, resulting in obstacles to QoS burst truncation [18] in switching nodes. The prioritized burst segmentation approach proposed in [10], which is different from most approaches, adopts the assembly of different priority packets into a burst in the order of de-creasing priorities. Should contention occur in switching nodes, the approach supports burst truncation rendering lower-priority packets toward the tail be dropped or deflected with higher probability. The approach achieves low packet loss probability for high-priority classes, with the price of excessive complexity paid during burst scheduling in switching nodes.

OBS gains the benefits of OCS and OPS. However, its offset-time-based design results in three complications. First, the de-termination of the offset time is a design dilemma. A large offset time incurs excessive packet delay. A small offset time may fail to make wavelength reservation prior to the burst arrival. This fact renders deflection routing (via longer paths) infeasible during contention resolution. Second, to enable efficient reser-vation of wavelengths, JET-based OBS requires the offset-time and burst length information to be included in the control packet, to provide a switch with the exact time and duration that the burst arrives and lasts, respectively. At each switching node along the path, such information needs to be maintained for fu-ture configuration until the burst arrives. Besides, the offset time is required to be decremented at every switching node and the burst length needs to be updated should burst truncation occur. Evidently, such design results in significantly increased com-plexity [19]. Third, the inclusion of the burst length information in control packets, together with the near-far problem described above, OBS gives rise to a difficulty in supporting QoS burst truncation. For example, consider a case that there is a high-pri-ority burst that arrives after a low-prihigh-pri-ority burst and potentially collides with the low-priority burst. If the control packet of the low-priority burst has already departed, its length can no longer be updated. In this case, the switching node is left no choice but to truncate the high priority rather than the low-priority burst. We refer to this type of operation as restricted QoS burst truncation.

These three OBS design complications are the primary moti-vators behind the design of the optical coarse packet switching (OCPS) paradigm [20]. While OBS can be viewed as a more efficient variant of OCS; OCPS can be considered as a less stringent variant of OPS. Similar to OBS, OCPS is aimed at supporting all-optical per-burst switched networks, which are labeled-based [12], QoS-oriented, and either bufferless or with limited FDL-based buffers. Unlike OBS using offset-time-based out-of-band control, OCPS adopts in-band control in which the header and payload are together transported via the same wavelength. More specifically, in an OCPS network, IP packets belonging to the same loss class and the same destination are assembled into bursts at ingress routers. A header for a burst payload, which carries forwarding (i.e., label) and QoS (e.g., priority) information, is modulated with the payload based on our newly designed superimposed amplitude shift keying (SASK) technique [21]. Besides, they are time-aligned during

modulation via necessary padding added to the header. They are realigned in switching nodes should burst truncation occur. Such design eliminates the payload length information from the header, and thus as will be shown, facilitates restriction-free QoS burst truncation in switching nodes. The entire burst is then forwarded along a preestablished optical label switched path (OLSP). At each switching node, the header and payload are first SASK-based demodulated [21]. Each burst payload is switched according to the label information in the header. While the header is electronically processed, the burst payload remains transported optically in a fixed-length FDL achieving constant delay and data transparency.

The main focus of the paper is on QoS-enhanced traffic control exerted during packet burstification at ingress nodes, aiming at providing delay and loss class differentiations for OCPS networks. In our work, we assume optical switches are buffer-less and all wavelengths are shared using wavelength converters [3], [22]. Regarding delay performance, due to the absence of buffering delay in core switches, the end-to-end delay performance is solely determined by the burstification delay. Considering the assembly of packets from flows with dif-ferent delay requirements, the problem becomes the scheduling of these packets during burstification. At first thought, existing scheduling disciplines [23]–[25] are possible candidates. These schemes have placed emphasis on the design of scalable packet schedulers achieving fairness and delay guarantees. All packets follow the exact departure order that is computed according to virtual finishing times being associated with packets. Neverthe-less, in the case of burstification, considering tens or hundreds of packets in a burst, the exact position of packets within a burst is no longer relevant. Most existing scheduling schemes thus become economically unviable. Regarding loss perfor-mance, rather than exploring reactive contention resolution mechanisms [17], in this work we focus on the design of traffic shaping with QoS provisioning.

In this paper, we present a dual-purpose traffic control scheme, called -Scheduler/Shaper. Notice that from the packet burstification perspective, it is simply a timer and threshold combined scheme, where and are the max-imum burst size (packet count) and maxmax-imum burst assembly time, respectively. To provide delay class differentiation, for IP packet flows designated with delay-associated weights, -Scheduler performs packet scheduling and assembly into bursts based on their weights and a virtual window of size . The Scheduler exerts simple first-in first-out (FIFO) service within the window and assures weight-proportional service at the window boundary. The guaranteed delay bound for each delay class is quantified via the formal specification of a stepwise service curve [23]. We also demonstrate the mean delay and 99% delay bound for each delay class via simulation results.

To provide loss class differentiation, -Shaper facili-tates traffic shaping with a larger burst size assigned to a higher priority class. To examine the shaping effect on loss performance, we analytically derive the departure process of -Shaper. The aggregate packet arrivals are modeled as a two-state Markov modulated Bernoulli process (MMBP) with batch arrivals. Analytical results delineate that -Shaper

(3)

Fig. 1. ( ; )-Scheduler/Shaper system architecture.

yields substantial reduction in the coefficient of variation (CoV) of the burst interdeparture time. The greater the burst size, the more reduction in the CoV. Furthermore, we conduct extensive simulations on a 24-node ARPANET network to draw loss performance comparisons between OCPS and JET-based OBS. Simulation results demonstrate that, through burst size adjust-ment, -Shaper effectively achieves differentiation of loss classes. Essentially, owing to enabling restriction-free QoS burst truncation in switching nodes, OCPS is shown to achieve superior packet loss probability for a high-priority class, and facilitate better differentiation of traffic classes, compared to JET-based OBS.

The remainder of this paper is organized as follows. In Section II, we introduce the -Scheduler/Shaper system architecture. In Section III, we describe the -Scheduler design, the stepwise service curve, and show the worst and 99% delay bounds for each delay class. In Section IV, we present a precise departure process analysis for -Shaper to analytically delineate the shaping effect on departing traffic characteristics. In Section V, we demonstrate the provision of loss class differentiation, and draw packet loss comparisons be-tween OCPS and JET-based OBS via network-wide simulation results. Finally, concluding remarks are made in Section VI.

II. -SCHEDULER/SHAPERSYSTEMARCHITECTURE In any ingress node, incoming packets (see Fig. 1) are first classified on the basis of their destination, loss, and delay classes. Packets belonging to the same destination and loss class are assembled into a burst. Thus, a burst may contain packets belonging to different delay classes. In the figure, we assume there are destination/loss classes and delay classes in the system. For any one of destination/loss classes, say class , packets of flows belonging to different delay classes are assembled into bursts through -Scheduler/Shaper according to their preassigned delay-associated weights. De-parting bursts from any -Scheduler/Shaper are optically transmitted, and forwarded via their corresponding, preestab-lished OLSP.

Essentially, -Scheduler/Shaper is a dual-purpose scheme. It is a scheduler for packets, abbreviated as

-Scheduler, which performs the scheduling of dif-ferent delay class packets into back-to-back bursts. On the other hand, it is a shaper for bursts, referred to as -Shaper, which determines the sizes and departure times of bursts. They are discussed in Sections III and IV, respectively.

III. -SCHEDULER ANDDELAYQoS

In the -Scheduler system, each delay class is associated with a predetermined weight [23]. A higher delay priority class is given a greater weight, which corresponds to a more stringent delay bound requirement. In addition, we assume all packets are of fixed size of one unit. Generally, -Scheduler performs scheduling of packets in accordance with their weights and a

virtual window of size . The weight of a class corresponds to the maximum number of packets of the class that can be accom-modated in a window, or burst in this case. Such window-based scheduling allows simple FIFO service within the window and assures weight-proportional service at the window boundary. In the sequel, we present the design and algorithm, followed by the specification of the stepwise service curve from which the guar-anteed delay bound can be obtained.

A. Scheduling Design and Algorithm

Upon arriving, packets of different classes are sequentially inserted in a sequence of virtual windows. The window size, which is set as the maximum burst size, , together with the weight of a class, determines the maximum number of packets (i.e., quotas) from this class that can be allocated in a window. For a class, if there are sufficient quotas, its new packets are sequentially placed in the current window in a FIFO manner. Otherwise, its packets are placed in an upward window in accordance to the total accumulated quotas. A burst is formed and departs when the burst size reaches or the Burst Assembly Timer (BATr) (set as initially) expires. For convenience, class weights are normalized to the window size. Namely, , where is the normalized weight of class .

The operation of -Scheduler can be best explained via a simple example illustrated in Fig. 2. For ease of illustration, the normalized weights are set as integers in the example. Initially, five packets from three classes ( , and ) arrive at time 1, and four of them are placed in the first virtual window except due to having only one quota in a window. The BATr is activated and set as BATr . At the end of time 1, a burst of size packets departs. The same operation repeats until the end of time 4. Notice that there are four packets in the system, which are placed in three consecutive virtual windows. A burst is still generated at the end of time 4. This explains why the “virtual” window is named. Finally, at time 8, a burst of size three is generated due to time out of the BATr.

The detailed algorithm of -Scheduler is outlined in Fig. 3. First, the system performs the Initialization operation whenever the system changes from being idle to busy due to packet arrivals. The quota of each class is initialized as its normalized weight, and the BATr is activated and set to be the value of . The algorithm then asynchronously performs two tasks repeatedly: Arrival and Departure. The Arrival task

(4)

Fig. 2. ( ; )-Scheduler: an example.

Fig. 3. ( ; )-Scheduler: the algorithm.

handles the insertion (Enqueue) of newly arriving packets in ap-propriate virtual windows; whereas the Departure task removes (Dequeue) the generated burst from the queue. If the queue remains nonempty, the BATr is reset to the value. It is worth noting that the algorithm works under noninteger normalized weights which are practically the case in real systems.

B. Worst Delay Bound Guarantee-Stepwise Service Curve

The service curve specification [23], [25] has been widely used as a flexible methodology for resource allocation to sat-isfy diverse delay and throughput guarantees. Prevailing packet

Fig. 4. Concept of stepwise service curve.

scheduling schemes are mostly work conserving exhibiting con-tinuous-wise service curves. In contrast, the -Scheduler is a nonwork-conserving server, in which packets do not depart from the system before the burst is generated. Our objective is to characterize the stepwise nature of the service curve for the nonwork-conserving system, -Scheduler.

In the sequel, we first define the stepwise function and intro-duce the stepwise service curve guaranteed by a general server, . We then specify the stepwise service curve guaranteed for a delay class by -Scheduler in Theorem 1. We finally provide the worst delay bound in two different forms based on the theorem. Throughout this section, we assume that there are classes in the system, and the optical link capacity is packets/slot. For ease of description, the normalized weight of any class is assumed greater than or equal to one.

Definition 1: A stepwise function of time and delay , under jump and incremental interval , is defined as

and

, (1)

where is the th ascending point, defined as . Accordingly, a stepwise function is uniquely determined by three parameters, , and . The significance of such stepwise function is that it corresponds to a quasiconstant-bit-rate service, in which a fixed amount of service can be offered per every time period , after a minimum delay of time .

As depicted in Fig. 4, under a general server, , let de-note the amount of service actually received by a class at time . In addition, denote the time instant at which the received ser-vice exceeds times of service granularity, . Namely,

, for all . For example in Fig. 4, a amount of service corresponds to the finishing transmission of four packets. Due to batch service, server actually finishes a two-packet transmission at , and a total of six-packet trans-mission at . Thus, is equal to which is the earliest time upon which (four-packet) service has been received.

The problem of seeking guaranteed service becomes the de-termination of a stepwise function which is the greatest lower bound of all possible scenarios of . We call such function

(5)

the stepwise service curve, guaranteed by , defined as follows.

Definition 2: A stepwise service curve under and , guaranteed by general server , is defined as

(2)

where . The supremum of (2)

uniquely occurs at the minimum value of , denoted as . Notice that the above uniqueness and minimum properties of rest on the fact that, by fixing , function is monotonically increasing with ; and by fixing , the function is monotonically decreasing with . Our main goal is to determine the stepwise service curve guaranteed by -Scheduler for a class, say class . To this end, one way of approaching it is to find the minimum service amount achieved at any given time, i.e., to find -axis service amount for any given -axis time . Another way, which is what we adopt here, is to determine the maximum time required before a given service amount is received, i.e., to find -axis time value for any given -axis service amount. For rigorousness, the above statement is outlined in the next lemma.

Lemma 1: If server guarantees a stepwise service curve with taken by Definition 2. If for all stepwise

func-tions , defining by

(3)

then .

The Proof of Lemma 1 is in Appendix A. To find the step-wise service curve for class , we are to determine three param-eters, and . First, it is simple to perceive that service granularity for class is equal to the normalized weight, , of the class. Second, the worst time period that amount of service can be at least offered is the maximum burst assembly time, , plus the burst transmission time, namely, . There-fore, we arrive at . The problem left is to find , which is given in the following theorem, with the proof shown in Appendix B.

Theorem 1: A stepwise service curve guaranteed by

-Scheduler for class , is in which

, and .

Based on Theorem 1, we are now in the position to derive the worst delay bound for different delay classes of traffic. Notice that the work [23] provided an absolute delay bound, subject to the constraint that arriving packets are leaky-bucket regulated. In our work, due to the lack of traffic regulation, a time-indepen-dent delay bound is unachievable. In lieu, we provide the worst delay bound for each class in two forms.

In the first form, we present a time-dependent worst delay bound for a packet, given the class of the packet. As shown in Fig. 5, we delineate two guaranteed service curves for class 1 with and class 2 with , respectively, based on Theorem 1. Suppose the forth packet from the beginning of a busy period arrives at . According to the theorem, if the packet is of class 1 (class 2), the worst delay bound until packet

is served is . Accordingly, for

the th packet of class arriving at time from the beginning of a busy period, the worst delay bound is , where and are given in Theorem 1.

Fig. 5. ( ; )-Scheduler’s stepwise service curves for two classes.

Fig. 6. Worst delay bound of an observed packet in bulk arrival. (a) Under different values. (b) Under different values.

In the second form, we provide the worst delay bound of an observed packet (of one class) that arrives along with a bulk of packet arrivals that belong to any traffic classes. Based on The-orem 1, we plot in Fig. 6 the worst delay bound as a function of the normalized weight for the observed packet, under a bulk arrival of 25 packets (including the observed packet). We reveal from the figure that the worst delay bound dramatically declines as the class weight increases under all settings. Signifi-cantly, such worst delay bound is guaranteed irrelevant to the weight and class distributions of other packets that arrive in the same bulk. This partially illustrates the significance of service curve in providing delay and throughput guarantees.

(6)

Fig. 7. Delay QoS provision under various loads. (a) Mean delay. (b) 99% delay bound.

C. Delay QoS Provision

In addition to the deterministic worst delay bound, we also seek stochastic delay performance metrics to gain more insights into the effectiveness of the weight-based scheduling on delay QoS provisioning. To this end, we carried out event-based simu-lations in which the mean packet delay and 99% delay bound (in units of slots) were measured. In the simulations, we have four delay classes ( – ), with the weights set as 10, 6, 5, and 4 (or 40, 24, 20, and 16, normalized with respect to ). The system is served by a wavelength in a capacity of one 60-byte packet per slot time. Each of these four classes generate an equal amount of traffic based on a two-state ( and ) MMBP. In the MMBP, the probability of switching from state to

is equal to , and the probability of

having one packet arrival during state is equal to , under an offered load, . Accordingly, the burstiness of traffic is . To draw a comparison, a FIFO system was also exper-imented. Simulations are terminated after reaching 95% confi-dence interval. Simulation results are plotted in Figs. 7 and 8.

We observe from Fig. 7 that both mean delay and 99% delay bound of all classes increase with the offered load. Superior to the FIFO system that undergoes long delay/bound at high loads, -Scheduler invariably assures low delay/bound for high-priority classes (e.g., and ) at a cost of increased delay/bound for low-priority classes (e.g., ). In Fig. 8, we il-lustrate how the weight of a class can be adjusted to meet its

Fig. 8. Delay QoS provision via the weight adjustment. (a) Mean delay. (b) 99% delay bound.

delay/bound requirements. For example, as shown in Fig. 8(b), to meet a 99% delay bound guarantee of 200 slots for class , the weight of must be greater than 7, given the weights of three other classes of 6, 5, and 4, respectively.

IV. -SHAPER ANDDEPARTUREPROCESSANALYSIS For clarity purposes, we highlight the operation of

-Shaper, particularly the BATr part of the system in the sequel. A burst of size is generated and transmitted if the total number of packets reaches before the burst assembly time exceeds . Otherwise, a burst of size less than is gener-ated when BATr expires. The BATr is initialized as the value when it is activated or reset. The BATr is activated when the system is changed from being idle to busy due to new packet arrivals. The BATr is immediately reset when a burst departs leaving behind a nonempty queue.

A. Departure Process Analysis

In a -Shaper system, bursts are served (transported) by one wavelength and forwarded via the same OLSP. In the anal-ysis, we consider -Shaper a discrete-time single-server queueing system, MMBP/G/1, in which a time slot is equal to the transmission of a fixed-length packet. The aggregate packet arrivals are assumed to follow a two-state MMBP that allows batch arrivals at each state. The two states are the and

(7)

Fig. 9. ( ; )-Shaper: departure process analysis.

states, which correspond to high and low mean arrival rates, respectively. The MMBP is characterized by four parameters , where is the probability of changing from state to in a slot, and represents the prob-ability of having a batch arrival at state . For ease of de-scription, the state change probability is denoted as

. Namely, , and

. The batch sizes at state and possess distribu-tions and , with mean sizes and , respec-tively. Let represent the mean arrival rate (packets/slot) (i.e., the load), and the burstiness of the arrival process, we thus have

(4) Fig. 9 is drawn in aid of comprehension throughout the anal-ysis. There are five possible events that sequentially occur in a slot as follows: (1) arrival process state change, (2) begin-of-burst departure, (3) packet arrivals, (4) end-of-begin-of-burst departure, and (5) BATr activation/reset. While Events (1) and (2) occur at the beginning of a slot, Event (3) takes place at any time within a slot, and Events (4) and (5) occur at the end of a slot.

The departure process distribution consists of two parts: burst interdeparture time , and burst size distributions. The burst interdeparture time takes values which are integer multi-ples of a slot. It is defined as the interval from the end of a pre-vious burst to the beginning of the following burst. Our goal is to find the joint distribution of and , i.e., . To approach it, we first obtain the queue length distribution seen by departing bursts, based on an imbedded Markov chain anal-ysis placing the imbedded points at burst departure instants, as shown by the arrows in Fig. 9.

Define random variable to be the number of packets left behind by the th departing burst, say at time slot , under the condition that the arrival process is in state ( or ) at . Let random variable represent the number of packets that arrive during the burst interdeparture interval, under the condi-tion that the arrival process changes from state prior to the be-ginning of the interval, to state at the end of the interval. More-over, let random variable denote the number of packets that arrive during the transmission time of an -packet burst, namely

slots, under the condition that the arrival process changes from state prior to the beginning of the time interval, to state at the end of the interval.

Accordingly, we find that

(5)

where , and . In

(5), a nonnegative term within the parentheses corresponds to the departure of a full-size burst; whereas a negative value corresponds to the departure of a burst due to BATr expira-tion. Significantly, since BATr is reset or activated after the th burst departure time, and and

are independent of any events that occur prior to time index is hence an imbedded Markov chain.

Based on (5), we can derive the limiting distributions of the queue length seen by departing bursts, rather than at all points in time. Notice that fortunately, such distribution is sufficient enough to determine the departure process distribution. Before we proceed, let us first derive the distribution for the number of packets that arrive in any given interval. Let denote the probability that packets have arrived in an interval of slots, under the condition the arrival process changes from state

prior to the beginning of the interval, to state at the end of the interval. For , we immediately have . For can be recursively computed as

(6) where is the probability that the arrival process changes from state to state . The first term within the square bracket in (6) corresponds to that all packets arrive in the first slots and no packet arrives in the last slot. The second term represents a batch of packets that arrive in the last slot with probability .

(8)

With the “ ” sign removed, (5) can be expanded into three cases, as seen in (7) at the bottom of the page. Notice that is absent from the first case of (7) due to the fact that the interdeparture time is zero if a departing burst leaves behind a system with or more packets. We now compute the queue length distribution by first conditioning on the value of , and separating case one from cases two and three in (7), as

(8) where

(9) and

(10)

To proceed, we need to solve in

(10). It can be resolved by considering five cases depending on different ranges of and values as given in (11). First of all, in case (1) when , a full-size burst is immediately trans-mitted, yielding . Thus, the probability under is one. In case (2), when but , the total number of packets must exceed the first time at a particular slot be-fore the BATr expires. Namely, within an interval of less than , there arrives a total of packets, and exactly at this slot, a batch of packets arrives, making . As opposed to case (2), in case (3) BATr expires. That is, the total number of packets that arrive within an interval of is , and . Case (4) in (11) under corresponds to the termination of a busy period of the system. Notice that BATr is not activated until the arrival of the first batch with packets. This explains the term within the square bracket. Under such condition, this case becomes identical to that when a departing burst leaves behind a system with packets, with the probability shown before the product sign. Notice that, this probability can be obtained by applying cases (1) to (3) once, depending on the value. Com-bining the results from the cases discussed above, we have (11) at the bottom of the page.

With (6) and (8)–(11), the limiting queue length distribution under the arrival process being at state or , can be given by

(12) We are now in the position to determine the departure process distribution, . We consider four cases depending on dif-ferent and values. First, in Case I) when , it is clear that

Case I)

if

if (13)

Second, Case II) corresponds to the transmission of a full-size burst due to having a total of or more packets before the BATr expires. Hence, we obtain that

if if if (7) if if if if otherwise (11)

(9)

Case II) (see (14) at the bottom of the page). Third, in Case III) when , and , the total number of packets in the system exceeds exactly at the same time when the BATr expires. Otherwise, if , a burst of size less than

is transmitted due to BATr time-out. That means Case III) [see (15) at the bottom of the page]. Finally, under the last case when , the departing burst must have left an empty system , resulting in the deactivation of the BATr. The timer remains deactivated until the arrival of the first batch of packets. Then, whether the next departing burst is a full-size one or not depends on the total number of arriving packets, as

Case IV) [see (16) at the bottom of the page]. Combining (13)–(16), we achieve the joint-form departure process distribution.

B. Numerical Results

We carried out analytic computation and event-based simu-lation to validate the analysis and capture the departure process behavior under various parameter settings and traffic arrivals. Analytical and simulation results of the queue length distri-bution and departure process distridistri-butions (interdeparture and burst size distributions) are shown in Figs. 10 and 11, respec-tively. In the MMBP, we adopt

and at load 0.6; and and

at load 0.8. The batch size in any of states and was uniformly distributed between 1 and 9. Accordingly, the bursti-ness of traffic is under both loads.

First, all analytical results are in profound agreement with simulation results. Interestingly, we discover from Fig. 10 that there are some spikes at queue-length in the queue length distribution. The phenomenon is caused by the maximum batch size of 9 in the arrival process. In addition, we observe that the interdeparture time distribution is sensitive to and . Under a high load condition, we observe the interdeparture time of zero burst size occurs with the largest probability under all values. The second largest probability for different settings occurs at the interdeparture time being

Fig. 10. System queue length distribution. (a) Medium load (0.6). (b) High load (0.8).

equal to the corresponding value, as shown by the spikes in Fig. 11(a).

To examine the effectiveness of shaping, we further compute the coefficient of variation (CoV) for the interdeparture time and burst size, under three values ( and ) and various

MMBP arrivals ( and and ).

Notice that the setting of corresponds to a FIFO system

if if (14) if if (15) if if (16)

(10)

Fig. 11. Departure process distributions. (a) Interdeparture time (~t) distribution. (b) Burst size(~s) distribution.

with no shaping. Numerical results are plotted in Figs. 12 and 13.

As shown in Fig. 12, as expected, the CoV of the interde-parture time increases with the offered load. Crucially, under any MMBP arrival, we discover that the CoV declines signif-icantly with larger values, yielding substantial reduction in burst loss probability. This fact will be again revealed in the network-wide simulation results presented in the next section. Moreover, we observe from Figs. 12 and 13 that the burstiness and batch size of the original MMBP arrival has an impact on any of the CoVs—the higher the burstiness and batch size, the greater the CoV. Nevertheless, the impact is insignificant com-pared to the effect of using different and values. As dis-played in Fig. 13, the CoV of the burst size declines with larger values under any MMBP arrival. Notice that greater values imply larger burst sizes, namely, better shaping effect.

V. LOSSQoS PROVISION ANDPERFORMANCECOMPARISON In this section, we demonstrate the performance of

-Shaper from three aspects: 1) traffic shaping effect on loss performance; 2) loss QoS provisioning for OCPS networks; and 3) loss QoS performance comparison be-tween the OCPS and the JET-based OBS [9] networks. For ease of description throughout the section, we refer to the three networks—OCPS without -Shaper, OCPS with

Fig. 12. CoV of the interdeparture time. (a) Under differentB and values. (b) Under different batch sizes and values.

-Shaper, and JET-based OBS, as the baseline, OCPS, and OBS networks, respectively.

Rather than considering one single switching node, we have simulated an entire optical network with QoS burst truncation and full wavelength conversion capabilities equipped in each switching node. The network we used in the experiment is the well-known ARPANET network [26] with 24 nodes and 48 links, in which 14 nodes are randomly selected as edge nodes. OLSP routing is subject to load balance of the network. Each link has up to 100 wavelengths, transmitting at 1 Gb/s, or one 60-byte packet per slot of duration 0.48 s. In simulations, departing bursts from ingress nodes can be served by any free wavelength, though, only after the previous burst has been fully transmitted. We measure two performance metrics—burst and packet loss probabilities. The burst loss probability is measured when QoS burst truncation is disregarded, i.e., the entire burst is dropped as a result of no free wavelength. Otherwise, the packet loss probability is computed.

In simulations, we generate packets according to the MMBP

with , and the batch size in both and

states being uniformly distributed between 1 and 9 . For a given load according to (4), traffic burstiness is then uniquely determined by . We adopt three different burstiness ( and ) in simulations. For comparison, we also generate Binomial-distributed arrivals that have been used to model smooth traffic. The probability that a packet arrives at

(11)

Fig. 13. CoV of the burst size. (a) Under differentB and values. (b) Under different batch sizes and values.

each slot is equal to the mean load , yielding a total offered load of , where is the number of wavelengths. Simulations are terminated after reaching 95% confidence interval. In the sequel, we explore these three aforementioned aspects in the three subsections, respectively.

A. Traffic Shaping Effect

To examine the traffic shaping effect, we draw a comparison of burst loss probability between the baseline and OCPS net-works. Simulation results are plotted in Fig. 14. We first observe from the figure that the results are consistent with our previous analytic CoV results—the greater the value, the lower the CoV and the burst loss probability. As shown in Fig. 14(a), com-pared with the baseline no-shaping network under MMBP ar-rivals, the OCPS network achieves more than five orders of mag-nitude reduction in burst loss probability under

, and and below. Compared to smooth Binomial arrivals, the OCPS network with traffic shaping still yields sev-eral orders of magnitude improvement in burst loss probability. As shown in Fig. 14(b), we discover that the improvement of loss probability is even more compelling in the presence of a large number of wavelengths due to higher statis-tical multiplexing gain.

Fig. 14. Traffic shaping effect: a comparison between the OCPS and baseline networks. (a)W = 50. (b) W = 100.

B. Loss QoS Provisioning

For OCPS networks, -Shaper facilitates loss QoS pro-visioning at edge nodes by means of burst size adjustment. Higher priority classes are assigned larger burst sizes. Notice that in parallel, each switching node within the network per-forms QoS burst truncation in the absence of free wavelengths. Specifically, an arriving high-priority burst that finds no free wavelength will preempt a burst that is of lower priority (than the arriving burst’s priority), and that has the least amount of data left unsent. Namely, the preemption is made on a “least-harm” basis.

In simulations, other than the parameters described above, we employ three traffic classes. They are Classes and , in the order of decreasing loss priorities. Each of these three classes generates an equal amount of MMBP traffic into the network. Notice that, to gain more insights into loss perfor-mance for networks with reasonable wavelength-based statis-tical multiplexing gain, we adopt 50 wavelengths in this sim-ulation. As a result, the packet loss probability for Class becomes too low to be measured within affordable time pe-riods. Though, it is sufficient to show the packet loss behavior for both Classes and . Simulation results are shown in Figs. 15 and 16.

(12)

Fig. 15. ( ; )-Shaper: loss performance under different loads. (a) Changing of the burst size of ClassH. (b) Changing of the burst size of Class M.

In Fig. 15, we show the packet loss probabilities of both Classes and , as a function of offered load under three dif-ferent burst sizes of Class [in Fig. 15(a)] and Class [in Fig. 15(b)]. As expected, the packet loss probability drastically increases with the load. Class traffic receives a higher grade of loss performance than Class traffic. Focusing on burst size adjustment, in Fig. 16 we plot the packet loss probabilities of Classes and as a function of the burst size of Class [in Fig. 16(a)] and Class [in Fig. 16(b)]. We discover a win–win phenomenon from the figure that, by increasing the burst size of Class , the packet loss probabilities for both Classes and (and Class ) decline noticeably. This is because since Class experiences better loss performance due to the use of a larger burst size (better shaping effect), Class makes less preemp-tion toward Classes and traffic. As shown in Fig. 16(a), due to the “least-harm” preemption guideline, Class with a larger size becomes less likely to be truncated than Class with a smaller size , and thus results in greater reduc-tion in packet loss probability. In contrast, suffering from pre-emption, Class undergoes invariably poor packet loss prob-ability particularly at high load 0.9. By furthermore increasing the burst size of Class , as shown in Fig. 16(b), we observe more reduction in packet loss probabilities for both Classes and . In this case, Class benefits from being less frequently preempted by Class , and thus experiences more performance improvement than that in the previous case.

Fig. 16. ( ; )-Shaper: loss QoS provision via burst size adjustment. (a) Changing of the burst size of ClassH. (b) Changing of the burst size of ClassM.

C. OCPS and OBS Performance Comparison

As was mentioned, owing to the near-far problem and header-payload decoupling design, a JET-based OBS network supports

restricted QoS burst truncation, resulting in loss performance

degradation for high-priority traffic classes. In this section, we focus on this issue by making a comparison of packet loss prob-ability between the OCPS and JET-based OBS networks. We carried out simulations on the same 24-node ARPANET net-work in which three traffic classes (Classes and ) were adopted. In simulations, each ingress node generates a total of 39 connections (three classes for each of 13 destination nodes) that follow different load-balancing OLSPs. For ease of com-parison, we use the same burst size for all three classes during

burstification, namely, .

For OCPS networks, we conduct QoS burst truncation in switching nodes on priority plus least-harm-preemption bases. For OBS networks, the offset time assigned to a burst is the total control packet processing time (path-dependent) plus the extra delay , where is the maximum burst transmission time (e.g., 48 s for ), and is

or for Classes , respectively. Notice that, in the OBS work reported in [9], the burst length is assumed exponentially distributed, and is assigned as the mean burst

(13)

Fig. 17. OCPS and OBS loss performance comparison. (a) = = = 25 and = 48 s. (b) = = = 100 and = 48 s. (c) = = = 25 and = 9:6 s. (d) = = = 100 and = 9:6 s.

length. It thus requires a large offset time difference between any two adjacent classes, such as (6, 3, 0), to meet 95% of traffic isolation degree. In our simulations, we apply the same timer and threshold combined scheme to packet burstification for the OBS network. As a result, with given as the maximum burst transmission time, all three above extra-delay settings, namely, (6, 3, 0), (4, 2, 0), and (2, 1, 0), achieves 100% of traffic isolation degree. In addition, the header processing time at each switching node is assumed fixed. Finally, we employ restricted QoS burst truncation during contention for the OBS network. Specifically, truncation of bursts is also accomplished on priority plus least-harm-preemption bases, but restricted to those bursts whose control packets have not yet departed from the switch. Simulations results are displayed in Fig. 17.

In Fig. 17, we draw comparisons of packet loss probabilities of all three traffic classes between the OCPS and three variants of OBS networks using three extra-delay settings, respectively, under four cases set by two burst sizes and two header processing times ( s, s). First, we observe from the figure that the OCPS and OBS networks provide typically the same grade of loss performance for Classes and under all four cases. Significantly, we discover that,

compared to OCPS as shown in Fig. 17(a) and (c), OBS under-goes several orders of magnitude deterioration in packet loss performance for Class traffic particularly under a smaller

burst size, i.e., . Among the three

OBS variants, OBS using the smallest extra offset time difference invariably suffers from the poorest packet loss probability. Such performance degradation is caused by the near-far problem that exacerbates under a smaller burst size, a larger header processing time, and/or a smaller extra offset time difference. Under any of the conditions, the offset time of a Class- burst is more likely to be smaller than that of a Class- or Class- burst, resulting in failing to make earlier wavelength reservation for the burst. This fact accounts for the poorest performance for Class taking place under and s, as shown in Fig. 17(a). As the burst size increases and the processing time decreases, as shown in Fig. 17(b)–(d), the near-far problem is relaxed, yielding noticeable performance improvement for Class in OBS networks. As opposed to OBS, the in-band-con-trolled-based OCPS networks are shown to provide invariably superior packet loss probability for Class traffic, enabling effective facilitation of loss class differentiation.

(14)

VI. CONCLUSION

In this paper, we have proposed a dual-purpose, delay and loss QoS-enhanced traffic control scheme, called -Scheduler/Shaper, exerted at ingress nodes for OCPS IP-over-WDM networks. Providing delay class differentiation, -Scheduler assures each weight-based delay class a worst delay bound derived from the corresponding stepwise service curve; and a stochastic 99% delay bound obtained from sim-ulation results. In addition, -Shaper provides loss class differentiation by means of assigning larger burst sizes to higher priority classes. Through a precise departure process analysis of an MMBP/G/1 system, we have delineated that -Shaper effectively reduces the CoV of the burst interdeparture time, resulting a substantial reduction in burst loss probability. We have performed simulations on an ARPANET network to make loss performance comparisons between the OCPS with -Shaper and the JET-based OBS networks. Simulation results demonstrated that, due to the near-far problem, OBS undergoes several orders of magnitude increase in packet loss probability for Class traffic particularly under a smaller burst size. As opposed to OBS, the in-band-controlled-based OCPS network was shown to provide invariably superior packet loss performance for a high-priority traffic class, enabling effective facilitation of loss class differentiation.

APPENDIX A

Proof of Lemma 1: First, we denote stepwise function

as . Given time between interval , by Definition 1 and the definition of , we get the first inequality: . Since is monotonically increasing and , we have the second inequality: . Combining the two inequalities, we obtain . According to Definition 2, since there exists only one minimum , namely is thus lower bounded

by , namely .

Moreover, (2) leads to a fact that inequality holds

at , for all . From the definition of in

the lemma, which indicates that is the minimum making satisfied for all , for all stepwise functions including , we imply that is upper bounded by namely . Accordingly, the lemma is proved.

APPENDIX B

Proof of Theorem 1: With the focus placed on an observed

busy period of class , let be the first packet initiating the busy period, and represent the th packet of the ob-served busy period. Let denote the index of the window being served at time from the beginning of the busy period, and denote the index of the window in which is placed. We immediately have the boundary condition,

. According to the virtual-window service policy of -Scheduler, we get the following inequality:

(17)

Suppose after packet has been served, the total service

amount has first exceeded . We get ,

and . Since is greater than , packet

must have been served no later than the th window. In other words, one gets

(18) By summing (17) and (18), we arrive at

(19) Equation (19) can be described in words as that, in order to finish service amount , the total number of windows elapsed

is bounded by .

Moreover, due to the fact that the normalized weight of any class can be a noninteger value, the actual number of packets in a virtual window can be less, equal to, or greater than the window size, . Under the worst case, the maximum offered service in a total of windows can be easily computed as . In other words, with the maximum offered service divided by , we reach that will be placed at worst in the th burst. Considering the worst case, each burst is generated when the BATr expires. The maximum delay from the beginning of the busy period to the time service amount has been offered is bounded as

(20) By assigning the least upper bound of to , we have

Subtracting by where , we obtain

. By Lemma 1, the theorem is proved.

ACKNOWLEDGMENT

The authors deeply thank the anonymous reviewers for the valuable comments and suggestions that greatly improved the presentation of the paper.

REFERENCES

[1] B. Mukherjee, “WDM optical communication networks: Progress and challenges,” IEEE J. Select. Areas Commun., vol. 18, pp. 1810–1824, Oct. 2000.

[2] T. El-Bawab and J.-D. Shin, “Optical packet switching in core networks: Between vision and reality,” IEEE Commun. Mag., vol. 40, pp. 60–65, Sept. 2002.

[3] L. Xu, H. Perros, and G. Rouskas, “Techniques for optical packet switching and optical burst switching,” IEEE Commun. Mag., vol. 39, pp. 136–142, Jan. 2001.

[4] F. Callegati, G. Corazza, and C. Raffaelli, “Exploitation of DWDM for optical packet switching with quality of service guarantees,” IEEE J.

Select. Areas Commun., vol. 20, pp. 190–201, Jan. 2002.

[5] L. Xu, H. Perros, and G. Rouskas, “The perspective of optical packet switching in IP dominant backbone and metropolitan networks,” IEEE

Commun. Mag., vol. 39, pp. 136–141, Mar. 2001.

[6] H. Dorren et al., “Optical packet switching and buffering by using all-optical signal processing methods,” J. Lightwave Technol., vol. 21, pp. 2–12, Jan. 2003.

(15)

[7] D. Hunter et al., “SLOB: A switch with large optical buffers for packet switching,” J. Lightwave Technol., vol. 16, pp. 1725–1736, Oct. 1998. [8] T. Battestilli and H. Perros, “An introduction to optical burst switching,”

IEEE Commun. Mag., vol. 41, pp. S10–S15, Aug. 2003.

[9] M. Yoo, C. Qiao, and S. Dixit, “Optical burst switching for service differ-entiation in the next generation optical internet,” IEEE Commun. Mag., vol. 39, pp. 98–104, Feb. 2001.

[10] V. Vokkarane and J. Jue, “Prioritized burst segmentation and composite burst-assembly techniques for qos support in optical burst-switched net-works,” IEEE J. Select. Areas Commun., vol. 21, pp. 1198–1209, Sept. 2003.

[11] J. Wei and R. McFarland, “Just-in-time signaling for WDM optical burst switching networks,” J. Lightwave Technol., vol. 18, pp. 2019–2037, Dec. 2000.

[12] C. Qiao, “Labeled optical burst switching for IP-over-WDM integra-tion,” IEEE Commun. Mag., vol. 38, pp. 104–114, Sept. 2000. [13] Y. Xiong, M. Vandenhoute, and H. Cankaya, “Control architecture in

op-tical burst-switched WDM networks,” IEEE J. Select. Areas Commun., vol. 18, pp. 1838–1851, Oct. 2000.

[14] M. Yoo, C. Qiao, and S. Dixit, “QoS performance of optical burst switching in IP-over-WDM networks,” IEEE J. Select. Areas Commun., vol. 18, pp. 2062–2071, Oct. 2000.

[15] A. Ge, F. Callegati, and L. Tamil, “On optical burst switching and self-similar traffic,” IEEE Commun. Lett., vol. 4, pp. 98–100, Mar. 2000. [16] M. Yuang, J. Shih, and P. Tien, “QoS burstification for optical burst

switched WDM networks,” in Proc. IEEE OFC, 2002, pp. 781–783. [17] L. Yang, Y. Jiang, and S. Jiang, “A probabilistic preemptive scheme

for providing service differentiation in OBS networks,” in Proc. IEEE

GLOBECOM, 2003.

[18] A. Detti, V. Eramo, and M. Listanti, “Performance evaluation of a new technique for IP support in a WDM optical network: Optical composite burst switching (OCBS),” J. Lightwave Technol., vol. 20, pp. 154–165, Feb. 2002.

[19] J. White, M. Zukerman, and H. Vu, “A framework for optical burst switching network design,” IEEE Commun. Lett., vol. 6, pp. 268–270, June 2002.

[20] M. Yuang, J. Shih, and P. Tien, “Traffic shaping for IP-over-WDM net-works based on optical coarse packet switching paradigm,” in Proc. Eur.

Conf. Optical Communication (ECOC), 2003.

[21] Y. Lin, M. Yuang, S. Lee, and W. Way, “Using superimposed ASK label in a 10 Gbps multi-hop all-optical label swapping system,” J. Lightwave

Technol., vol. 22, pp. 351–361, Feb. 2004.

[22] S. Danielsen, P. Hansen, and K. Stubkjaer, “Wavelength conversion in optical packet switching,” J. Lightwave Technol., vol. 16, pp. 2095–2108, Dec. 1998.

[23] A. Parekh and R. Gallager, “A generalized processor sharing approach to flow control in integrated services networks: The single-node case,”

IEEE/ACM Trans. Networking, vol. 1, pp. 344–357, June 1993.

[24] J. Bennett and H. Zhang, “WF Q: Worst-case fair weighted fair queueing,” in Proc. IEEE INFOCOM, 1996, pp. 120–128.

[25] D. Stiliadis and A. Varma, “Latency-rate servers: A general model for analysis of traffic scheduling algorithms,” IEEE/ACM Trans.

Net-working, vol. 6, pp. 611–624, Oct. 1998.

[26] H. Harai, M. Murata, and H. Miyahara, “Performance analysis of wave-length assignment policies in all-optical networks with limited-range wavelength conversion,” IEEE J. Select. Areas Commun., vol. 16, pp. 1051–1060, Sept. 1998.

Maria C. Yuang received the B.S. degree in applied

mathematics from the National Chiao Tung Uni-versity, Hsinchu, Taiwan, R.O.C., in 1978, the M.S. degree in computer science from the University of Maryland, College Park, in 1981, and the Ph.D. de-gree in electrical engineering and computer science from the Polytechnic University, Brooklyn, NY, in 1989.

From 1981 to 1990, she was with AT&T Bell Lab-oratories and Bell Communications Research (Bell-core), where she was a Member Of Technical Staff working on high-speed networking and protocol engineering. She was also an Adjunct Professor in the Department of Electrical Engineering, Polytechnic University, during 1989–1990. In 1990, she joined National Chiao Tung Univer-sity, where she is currently a Professor of the Department of Computer Science and Information Engineering. Her current research interests include optical and broad-band networking, wireless local/access networking, multimedia commu-nications, and performance modeling and analysis.

Po-Lung Tien received the B.S. degree in applied

mathematics, the M.S. degree in computer and in-formation science, and the Ph.D. degree in computer and information engineering from the National Chiao Tung University, Hsinchu, Taiwan, R.O.C., in 1992, 1995, and 2000, respectively.

In 2000, he joined National Chiao Tung University, where he is currently a Research Assistant Professor of the Department of Computer Science and Infor-mation Engineering. His current research interests in-clude optical networking, wireless local networking, multimedia communications, performance modeling and analysis, and applica-tions of soft computing.

Julin Shih was born in Taipei, Taiwan, R.O.C., in

1976. He received the B.S. degree in management and information systems from the National Central University, Chung-li, Taiwan, in 1999 and the M.S. degree in computer science and information engi-neering from the National Chiao Tung University, Hsinchu, Taiwan, in 2001, where he is currently pursuing the Ph.D. degree.

His currently research interests include high speed networking, optical networking, and performance modeling and analysis.

Alice Chen received the B.S. degree in electronics

engineering and the M.S. degree in computer science and information engineering from the National Chiao Tung University, Hsinchu, Taiwan, R.O.C., in 1984 and 1992, respectively.

Currently, she is a Senior Engineer at Computer and Communications Research Laboratories of Industrial Technology Research Institute, Hsinchu, where she works on network control and manage-ment of optical networks.