Performance Evaluation for Minislot Allocation for Wireless Mesh Network

Performance Evaluation for Minislot

Allocation for Wireless Mesh Networks

Mohsen Guizani, Senior Member, IEEE, Phone Lin, Senior Member, IEEE,

Shin-Ming Cheng, Member, IEEE, Di-Wei Huang, and Huai-Lei Fu

Abstract—The IEEE 802.16 Standard defines the mesh mode for

media access control for external and internal packet transmis-sion. In the IEEE 802.16 mesh mode, the allocation of minislots is handled by centralized scheduling and distributed schedul-ing, which are independently exercised. This paper proposes the Combined Distributed and Centralized (CDC) and Combined Distributed and Centralized with Queue capability (CDCQ) schemes to combine distributed scheduling and centralized scheduling so that the minislot allocation can be more flexible and the utilization is increased. Two scheduling algorithms, i.e., the Round-Robin (RR) and Greedy algorithms, are used as the baseline algorithms for centralized scheduling. This paper pro-poses an analytical model and conducts simulation experiments to investigate the performance of the CDC-series schemes with the RR and Greedy algorithms in terms of the acceptance rate of both external and internal packet data. Our study indicates that the CDC-series schemes outperform the scheme proposed in the IEEE standard.

Index Terms—IEEE 802.16, minislot allocation, scheduling,

wireless mesh network (WMN).

NOMENCLATURE

α Maximum percentage of minislots that can be allocated for external packets in a data subframe for the Partition scheme.

δA Delay bound for the internal packets.

δI Delay bound for the external packets.

λA Internal packet arrival rate to an SS.

λI External packet arrival rate to an SS.

1/μA Expected internal packet transmission time.

1/μI Expected external packet transmission time.

Manuscript received May 17, 2007; revised October 27, 2007, November 17, 2007, December 16, 2007, and January 16, 2008. First published February 15, 2008; current version published November 12, 2008. The work of P. Lin was supported in part by the National Science Council (NSC), R.O.C., under Con-tract NSC-96-2627-E-002-001, ConCon-tract NSC-96-2811-E-002-010, ConCon-tract NSC-96-2628-E-002-002-MY2, and Contract NSC-95-2221-E-002-091-MY3, Ministry of Economic Affairs (MOEA), R.O.C., under Contract 93-EC-17-A-05-S1-0017, the Telcordia Applied Research Center, Taiwan Network Infor-mation Center (TWNIC), the Excellent Research Projects of National Taiwan University under 95R0062-AE00-07, and the Chunghwa telecom M-Taiwan program M-Taoyuan Project. The review of this paper was coordinated by Prof. B. Mark.

M. Guizani is with the Department of Computer Science, Western Michigan University, Kalamazoo, MI 49008-5201 USA (e-mail: mguizani@ cs.wmich.edu).

P. Lin, D.-W. Huang, and H.-L. Fu are with the Department of Computer Science and Information Engineering, National Taiwan University, Taipei 106, Taiwan, R.O.C. (e-mail: plin@csie.ntu.edu.tw; dwhuang@pcs.csie.ntu.edu.tw; vicfu@pcs.csie.ntu.edu.tw).

S.-M. Cheng is with the Department of Electrical Engineering, National Taiwan University, Taipei 106, Taiwan, R.O.C. (e-mail: smcheng@cc.ee.ntu. edu.tw).

Digital Object Identifier 10.1109/TVT.2008.918712

K Number of layers in the centralized scheduling tree. M Total number of minislots in a data subframe.

mA Number of minislots an internal packet requests for

transmission.

mI Number of minislots an external packet requests for

transmission.

PA,d Dropping probability for the internal packet.

PI,d Dropping probability for the external packet.

ts Length of a scheduling period.

vλA Variance of Gamma distributed internal packet

interar-rival times.

vλI Variance of Gamma distributed external packet

interar-rival times.

vμA Variance of Gamma distributed internal packet

trans-mission times.

vμI Variance of Gamma distributed external packet

trans-mission times.

I. INTRODUCTION

T

HE IEEE 802.16 Standard [1] (also known as WiMax) defines air interface, including the physical and media access control (MAC) layers, for wireless metropolitan area networks. It provides fixed broadband wireless access with the same level of quality of service as the traditional cabled access network, e.g., fiber optical links, coaxial links, and digital sub-scriber line links. The data transmission rate is up to 70 Mb/s. An IEEE 802.16 network consists of base stations (BSs) and subscriber stations (SSs). The BS serves as a gateway between the IEEE 802.16 network and the external network. The SS acts like a client-side terminal through which mobile users can access the network. The IEEE 802.16 network operates at the 10–66 GHz or the 2–11 GHz band [1], [2]. In the 10–66 GHz band, the signal propagation between a BS and an SS is through line of sight (LOS). The 2–11 GHz band supports non-LOS communication. The IEEE 802.16 Standard specifies two modes for sharing the wireless medium: 1) the point-to-multipoint (PMP) mode and 2) the mesh mode. The PMP mode is designed for wireless communication between the BS and the SSs, and the mesh mode enables communication among SSs [1], [3]. In this paper, we concentrate on studying the mesh mode. To simplify our description, we refer to the IEEE 802.16 Standard, with the mesh mode as the wireless mesh network (WMN).

Fig. 1(a) shows the WMN network architecture. The mesh BS connects to the external network with backhaul links. Any SS pair without direct wireless links can relay the data to 0018-9545/$25.00 © 2008 IEEE

Fig. 1. IEEE 802.16 mesh network architecture. (a) Network topology. (b) Scheduling tree with index numbers.

Fig. 2. Frame structure in the IEEE 802.16 mesh network.

Fig. 3. Example for the minislot reuse property.

each other through other SSs. The users connect to the SS by adopting various existing local area network technologies, e.g., IEEE 802.3 (Ethernet) [4] or IEEE 802.11 (WiFi) [5]. In this paper, we focus on the MAC protocol between the SSs and between the SS and the mesh BS. The WMN adopts the time-division multiplexing (TDM) radio access technology between SSs and between the SS and the mesh BS, where a radio channel is divided into physical slots (PSs) using time sharing, and mul-tiple PSs are grouped as a frame. As shown in Fig. 2, a frame is divided into a control subframe and a data subframe. The control subframe consists of transmission opportunities (TOs) used to carry signaling messages for centralized scheduling and distributed scheduling (to be discussed later), which are denoted as TOc and TOd, respectively. The numbers of TOcs

and TOds in a control subframe are configured by the operator.

The data subframe carries the user data, which is further divided into at most 256 minislots [1]. The transmission rate r (in bits per second) of a minislot depends on several factors (e.g., channel coding, modulation, and frequency band). More details about the discussion of these factors are available in [1]. A minislot can be reused by multiple SSs (i.e., multiple SSs may transmit packets in the same minislot), as long as the SSs are geographically separated [6], [7] (i.e., they do not interfere with each other). For example, in Fig. 3, SSa1and SSa4can transmit

data to SSa2 and SSa3 in the same minislot, respectively. This

property is called “minislot reuse” in TDM.

The IEEE 802.16 Standard proposes centralized scheduling and distributed scheduling for minislot allocation. In central-ized scheduling, the mesh BS works like a cluster head that maintains the topology of WMN, receives the minislot

allo-cation request from each SS, and determines transmission and reception minislots for each SS. Thus, all the control and data packets need to go through the mesh BS. Distributed scheduling is exercised in two neighboring SSs to reserve minislots for data transmission between them. The data traffic in the WMN can be divided into two categories: 1) external traffic (routed between the SS and the application server out of WMN) and 2) internal traffic (routed between two SSs in the same WMN). A data subframe can simultaneously carry the internal traffic packets and the external traffic packets. Since the external traffic should be routed in WMN and then delivered to the application server through the mesh BS, and the internal traffic only occurs between two SSs within the WMN, it is desirable to adopt centralized scheduling and distributed scheduling to allocate minislots for the external and internal traffic, respectively.

The IEEE 802.16 Standard suggests that the data sub-frame be partitioned into two parts. In this standard [1], the MSH_CSCH_DATA_FRACTION parameter is defined to store the proportion of minislots allocated to centralized schedul-ing and distributed schedulschedul-ing, which is carried in the mesh network configuration (MSH-NCFG) message. This implies that the minislots in a data subframe are separately allocated to centralized scheduling and distributed scheduling. In [1], it is mentioned that centralized scheduling and distributed scheduling can be executed in the same data subframe.

This implies that the data subframe is partitioned into two parts to serve the external and internal traffic, respectively, and is known as the “Partition” scheme. However, this may not be the best solution, because the partition boundary may not precisely capture the traffic pattern and the minislots may not be fully utilized. The two main objectives of this paper are given as follows:

1) developing the Combined Distributed and Centralized (CDC) and Combined Distributed and Centralized with Queue capability (CDCQ) schemes to break the partition

boundary so that the minislot allocation can be more flexible;

2) proposing an analytical model and conduct simulation ex-periments to investigate the performance for the Partition, CDC, and CDCQ schemes.

A. Literature Review

The related literature for the minislot allocation of WMN is summarized as follows: In [8], Wei et al. targeted design-ing a greedy-like algorithm and a routdesign-ing path establishment algorithm for only centralized scheduling. In [9], Kim and Ganz proposed an algorithm based on the weights of SSs to fairly allocate minislots for SSs to deliver the external traffic (i.e., for only centralized scheduling). In this paper, they investigated the fairness for minislot allocation. In [10], Chen et al. considered only centralized scheduling, where they proposed an odd–even alternation mechanism for minislot allocation. The three papers considered only centralized scheduling. They did not consider the interaction of centralized scheduling and distributed scheduling. Furthermore, there is no complete performance analysis in these studies. Therefore, the two ideas being investigated in this paper are CDC and CDCQ. The study in [11] focused on the design of the centralized scheduling algorithm. This is beyond the scope of this paper. In [12], Cao et al. discussed the performance evaluation for distributed scheduling. The interaction and combination of the distributed scheduling and the centralized scheduling are not considered in [12]. In this paper, we consider and provide a more complete performance evaluation for minislot allocation in WMNs.

The rest of this paper is organized as follows: Section II first illustrates distributed scheduling and centralized scheduling, and then presents the Partition scheme in the IEEE 802.16 Standard and the proposed CDC schemes. An analytical model, simulation experiments, and performance evaluation are given in Section III. Finally, Section IV concludes our study.

II. PARTITION ANDCDC SCHEMES

Let SSai denote an SS with node ID ai. Assume that the

total number of minislots in a data subframe is M . The variable sj indicates the status of the jth minislot in a data subframe.

sj= F indicates that the minislot is fresh, sj = TX indicates

that the minislot is used to transmit data, and sj= RX indicates

that the minislot is used to receive data. SSai maintains its

own array Sai={s1, s2, s3, . . . , sM} to store the status of each

minislot, i.e., how it functions in that minislot.

Upon receipt of an internal packet request (requesting trans-mission rate RA,auto be transmitted to SSau’s neighbor SSav),

SSau exercises a three-way handshaking procedure with SSav

to select RA,au/r collision-free

1 _{minislots to transmit the}

packet. The three-way handshaking procedure is known as “distributed scheduling,” the details of which can be found 1_{The kth minislot in the data subframe is called “collision free” if it satisfies} the following two properties: 1) sk= RX for all neighbors of SSau and

2) sk= TX for all neighbors of SSav.

in our previous work [13]. Note that distributed scheduling introduces a delay for the transmission of packets due to the coordination among SSs.

For data communication between the mesh BS and the SSs, the IEEE 802.16 Standard proposes centralized scheduling, where the mesh BS acts as a scheduler and determines trans-mission and reception minislots for each SS. A scheduling tree rooted at the mesh BS (i.e., the routing path between each SS and the mesh BS) is established. Upon receipt of an external packet request (requesting transmission rate RI,ai to

be transmitted to the mesh BS), SSaiand the mesh BS exercise

the centralized scheduling procedure to reserve transmission rate RI,ai in all SSs along the routing path from SSai to the

mesh BS.

The centralized scheduling consists of three stages. In the first stage, each SS buffers all external packet requests. In the second stage, each SS forwards buffered requests to the mesh BS. The mesh BS executes the scheduling algorithms (to be discussed later) to check the status arrays S’s of all SSs along the routing path from SSai to the mesh BS and tries to reserve

enough collision-free minislots in all SSs along the routing path, which is known as the “scheduling result.” Take Fig. 1 as an example. Each SS (along the routing path from the SSa4 to

the mesh BS, i.e., SSa4and SSa1) requiresRI,a4/r

collision-free minislots to serve the external packet request. In the third stage, the mesh BS distributes the scheduling result to all SSs, and the SSs reserve minislots according to the result. The time period for exercising the three stages is defined as a scheduling period (denoted as ts). The minislots of all SSs are re-reserved

by centralized scheduling at the beginning of every scheduling period. The scheduling result in the ith scheduling period is ref-erenced in the (i + 1)th scheduling period, as shown in Fig. 2.

In the centralized scheduling, the minislot utilization is highly dependent on the scheduling algorithm. To date, some studies [11], [14], [15] have touched on this issue. It has been shown that the scheduling algorithm is an NP-hard problem, i.e., we may not find the optimal solution for scheduling when the number of SSs in a WMN is sufficiently large. In [11], it has been proven that, under certain WMN network conditions, the centralized scheduling is no longer an NP-complete problem. In this paper, we use the two general algorithms Round-Robin (RR) and Greedy as the baseline centralized scheduling algo-rithms (that have widely been adopted to solve many scheduling problems and are easily deployable in real systems) to investi-gate the performance of the centralized scheduling. The two algorithms will be described in Appendix I.

As suggested by the IEEE 802.16 Standard [1], the minislots in a data subframe are partitioned for both distributed schedul-ing and centralized schedulschedul-ing. In this paper, we refer to this operation as the Partition scheme. The possible implementation for the Partition scheme is elaborated.

Partition Scheme. The minislots in a data subframe are parti-tioned into two parts: one for the centralized scheduling and the other for the distributed scheduling. The centralized scheduling and distributed scheduling are independently executed. Each SS maintains a first-in–first-out (FIFO) queue reqlist to buffer the external packet requests arriving at the SS during the scheduling period. The Partition scheme consists of six

Fig. 4. Flow chart for the Partition scheme. (a) Arrival. (b) Request. (c) Transmission. (d) Departure.

Fig. 5. Examples for minislot allocation for (a) Partition and (b) CDC schemes. procedures: Initial, Arrival, Request, Schedule, Transmission, and Departure.

1) Initial. This procedure initiates the system parameters. The mesh BS broadcasts to all SSs the number Mc of

minislots in a data subframe that can be allocated for centralized scheduling.

2) Arrival. See Fig. 4(a). This procedure is exercised when a new packet request arrives during the scheduling period. The SS checks the type of request [see (1) in Fig. 4(a)]. If it is an external packet request, the SS buffers this request in reqlist [see (2) in Fig. 4(a)]. If it is an internal packet request, the SS immediately executes the distributed scheduling to reserve minislots for this request [see (3)–(5) in Fig. 4(a)]. Then, the internal packet can be transmitted in the reserved minislots [see (6) in Fig. 4(a)]. 3) Request. See Fig. 4(b). At the end of the scheduling period, each SS executes the Request procedure to reserve minislots for external packet transmission during the next scheduling period. Suppose that, at the end of the schedul-ing period, there are paiexternal packet requests buffered

in the reqlist and qai external packets being served in

SSai during the current scheduling period. SSai sends

the centralized scheduling request message carrying the number pai+ qaito the mesh BS.

4) Schedule. After the mesh BS receives the centralized scheduling requests from all SSs, it executes the Schedul-ing procedure. The mesh BS releases all minislots for centralized scheduling by setting their status to F. Then, it executes the centralized scheduling algorithm (see

Appendix I) to reserve minislots for the pai+ qaiexternal

packet requests. The mesh BS sends the scheduling result to all SSs.

5) Transmission. See Fig. 4(c). When an SS SSai receives

the scheduling result from the mesh BS, SSai executes

this procedure to transmit external packets in the assigned minislots. Suppose that p_ai+ q_aiexternal packet requests are granted to be served [see (1) in Fig. 4(c)]. Then, SSai

drops pai+ qai− pai− q



ai external packets [see (2) in

Fig. 4(c)] and transmits p_ai+ q_a_i external packets in the reserved minislots [see (3) in Fig. 4(c)].

6) Departure. See Fig. 4(d). This procedure is invoked in each SS when a packet transmission completes. If the type of the packet is an internal packet, the SS releases the minislots serving this packet by setting their status to F [see (2) in Fig. 4(d)]. If it is an external packet, the procedure does nothing, i.e., the status of the minislot is unchanged during the current scheduling period.

Fig. 5(a) shows an example of the scheduling result of the Partition scheme, where the minislots in a data subframe are labeled as M S1, M S2, . . . , M S256.

In the Partition scheme, once the WMN is configured, the minislots cannot be flexibly reserved for the centralized scheduling and distributed scheduling until the next configu-ration. We propose the CDC scheme to release the aforemen-tioned limitation, whose details are given here.

CDC Scheme. In this scheme, the partition boundary is removed, and both distributed scheduling and centralized scheduling can allocate all minislots in a data subframe. We

Fig. 6. Flow chart for the CDC scheme. (a) Request. (b) Transmission. (c) Departure. slightly modify the procedures of the Partition scheme. Due to the delay of the process for the three-way handshake, the trans-mission for the internal packet request may not be completed within a scheduling period. Thus, each SS maintains a FIFO queue servqueue to buffer the internal packets, which are not completely transmitted in a scheduling period. The queued external packets can be served in the next scheduling period. If the time period when internal packet requests wait in the servqueue is longer than a delay bound δA, these packets are

dropped. The four procedures are modified as described here. 1) Arrival. The procedure is similar to that of the Partition

scheme. For an external packet request, the SS buffers this request in reqlist. For an internal packet request, the SS immediately executes the distributed scheduling to reserve minislots for this request. The SS can allocate the total minislots to internal packet requests without boundary.

2) Request. See Fig. 6(a). At the end of the scheduling period, SSai sends the centralized scheduling request

message containing the number pai+ qaito the mesh BS

[see (1) in Fig. 6(a)]. Then, SSai queues all the internal

packets currently being served into servqueue [see (2) in Fig. 6(a)].

3) Schedule. The mesh BS schedules the total M minislots in a data subframe to serve external packet requests by exercising the centralized scheduling algorithm (to be elaborated upon in Appendix I).

4) Transmission. See Fig. 6(b). This procedure is similar to that of the Partition scheme. The difference is described as follows: Each SS transmits the external packet first and then serves the internal packets in servqueue by execut-ing distributed schedulexecut-ing [see (4)–(9) in Fig. 6(b)]. 5) Departure: See Fig. 6(c). When an internal packet

trans-mission is complete [see (1) and (2) in Fig. 6(c)], the SS takes the same actions in the Transmission procedure. Note that, in the CDC scheme, the minislots are first allocated to the external packets by centralized scheduling at the beginning

of every scheduling period. During the scheduling period, if internal packet requests arrive, the left minislots are allocated to these requests by distributed scheduling. Fig. 5(b) shows an example for minislot allocation with the CDC scheme.

CDC takes higher priority to serve external packets than internal packets. We propose an enhanced scheme CDCQ to increase the acceptance of the internal packets. In CDCQ, two FIFO queues IQ and AQ are maintained in each SS to buffer the dropped external packet requests and the dropped internal packet requests, respectively. The dropped requests can temporarily be buffered in IQ and AQ and may be served in the following scheduling periods. If the external (internal) packet requests in IQ(AQ) wait longer than a delay bound δI(δA) for

the external (internal) packets, the requests are dropped. Note that the IEEE 802.16 Standard defines the two mes-sages mesh centralized scheduling (MSH-CSCH) and mesh centralized schedule configuration (MSH-CSCF) to broadcast scheduling results to all SSs [1]. In the implementation for the CDC and CDCQ schemes, we may reutilize these two messages. Therefore, we do not introduce any new message types (or overhead) to the WMN.

In the rest of paper, to simplify our description, we use Partition_RR, Partition_Greedy, CDC_RR, CDC_Greedy, CDCQ_RR, and CDCQ_Greedy to denote Partition combined with RR and Greedy, CDC combined with RR and Greedy, and CDCQ with RR and Greedy, respectively.

III. PERFORMANCEEVALUATION

We conduct simulation experiments to investigate the per-formance of the Partition, CDC, and CDCQ schemes with the RR and Greedy algorithms. Our simulation model is based on the event-driven approach, which has widely been adopted to simulate the wireless network [16]–[20]. The notations used in the simulation experiments are listed in the Nomenclature list. Our study assumes that all SSs are identical. Following the IEEE 802.16 Standard [1], we model the WMN as a regular hexagonal topology, as shown in Fig. 7, where a four-layer

Fig. 7. Four-layer WMN layout structure.

WMN is considered. Comparing with the square-grid topology adopted in [21], it is more general to adopt a hexagonal topol-ogy to simulate the WMN.

Note that every IEEE 802.16 transmission includes two or three orthogonal frequency-division multiplexing (OFDM) symbols of overhead, which is specified in the physical layer [1]. Our work focuses on the performance of the minislot allo-cation for both centralized scheduling and distributed schedul-ing (i.e., the MAC layer). The detailed performance analysis for the physical layer of OFDM is beyond the scope of this paper since it has been treated in many previous studies (e.g., [22] and [23]).

Let layer-k SS denote an SS in layer k of the scheduling tree. In this topology, a layer-k SS is k hops (where k≥ 1) away from the mesh BS. There are 3k SSs in layer k.

We assume that an external packet and an internal packet request mI and mA minislots for data transmission,

respec-tively. Let α be the maximum percentage of minislots that can be allocated for external packets in a data subframe for the Partition scheme, where 0%≤ α ≤ 100%. Then, Mc=αM.

For the CDC-series schemes, all minislots can be allocated to the external packets.

We simulate 10 million packet arrivals in each experiment to ensure that the confidence interval of the 95% confidence level of the output measure is less than 3% of the mean value [24]. Let NI and NAbe the number of external and internal packet

arrivals in an SS, respectively. Let N_I(k) be the total number of external packet arrivals in layer-k SSs, and we have N_I(k)= 3kNI. Let N_I,d(k)be the total number of dropped external packet

arrivals (i.e., the packet arrival cannot be served) in layer-k SSs. The dropping probability P_I,d(k)for the external packet arrivals in layer-k SSs is obtained by P_I,d(k)= N (k) I,d N_I(k) = N_I,d(k) 3kNI . (1)

The dropping probability PI,dfor the external packet arrivals in

a K-layer WMN is obtained using PI,d= K k=13kP (k) I,d f (2)

where f = 3K(K + 1)/2 is the total number of SSs in a K-layer WMN. Let N(ai)

A,d be the number of dropped internal

packet arrivals in SSai. The dropping probability PA,d for the

internal packet arrivals in a K-layer WMN is calculated by

PA,d= f i=1N (ai) A,d f NA .

This study uses an analytical model to partially validate the simulation model, where we consider the minislot allocation in the external packets in the Partition_RR and CDC_RR schemes. In the analytical model, we assume that, in an SS, the external and internal packet arrivals form Poisson processes with rates λI and λA, respectively. Assume that the transmission times of

the external and internal packets are exponentially distributed with means 1/μI and 1/μA, respectively. By using exponential

assumptions, our analytical model can validate the simulation model where we consider general external and internal packet interarrival and transmission time distributions.

We use a K-dimensional (K-D) Markov process to model the minislot allocation for external packet requests for Partition_RR and CDC_RR. For the purpose of illustration, the analytical model for a four-layer WMN is presented. In the Markov process, a state (w, x, y, z) denotes that, in the WMN, there are w, x, y, and z external packets being served in layer-1, layer-2, layer-3, and layer-4 SSs, respectively.

In the Partition and CDC schemes, to serve an external packet arrival at a layer-k SS, other k− 1 SSs (whose layer numbers are lower than k) will relay the packet to the mesh BS. Each of the layer-(k− 1), layer-(k − 2), . . ., layer-2, and layer-1 SSs requires mI minislots to relay an external packet to the mesh

BS. With the RR algorithm, each minislot is allocated to at most one SS. For the Partition_RR and CDC_RR schemes, the total number of minislots required to serve an external packet arrival at a layer-k SS is kmI. The state space S for the Markov

process is S =  (w, x, y, z)|0 ≤ w + 2x + 3y + 4z ≤  αM mI  0≤ w ≤  αM mI  , 0≤ x ≤  αM 2mI  0≤ y ≤  αM 3mI  , and 0≤ z ≤  αM 4mI  . (3)

Let πw,x,y,zbe the steady-state probability for state (w, x, y, z).

By convention, πw,x,y,z = 0 if state (w, x, y, z) /∈ S. For all

legal states (w, x, y, z)∈ S, we have 

(w,x,y,z)∈S

πw,x,y,z = 1. (4)

Fig. 8 shows the state transition diagram for this Markov process. Due to page limitations, the description of the state transitions is omitted, and the transitions are listed in

Fig. 8. Markov chain for centralized scheduling in Partition_RR or CDC_RR. Appendix II. The balance equations for the Markov process are expressed as  δ+₁ + 2δ₃++ 3δ₅++ 4δ₇+3λI + wδ₂−+ xδ₄−+ yδ₆−+ zδ₈−μI  πw,x,y,z = (w + 1)μIδ2+πw+1,x,y,z+ (x + 1)μIδ+4πw,x+1,y,z + (y + 1)μIδ6+πw,x,y+1,z+ (z + 1)μIδ+8πw,x,y,z+1 + 3λIδ1−πw−1,x,y,z+ 6λIδ−3πw,x−1,y,z + 9λIδ5−πw,x,y−1,z+ 12λIδ7−πw,x,y,z−1. (5)

If an external packet request arrives at the layer-k SS at the state where w + 2x + 3y + 4z >αM/mI − k, the request

is dropped. Therefore, the dropping probability P_I,d(k) for the external packets in layer-k SSs is

P_I,d(k)= 

(w,x,y,z)∈Sandw+2x+3y+4z>αM mI

−k

πw,x,y,z. (6)

From (4)–(6), the steady-state probability πw,x,y,z and PI,d(k)

can be solved by using the successive overrelaxation method [25]. By applying (6) to (2), we can obtain PI,d. In Fig. 9, the

solid and dashed curves plot the analysis and simulation results for the PI,d performance for Partition_RR, respectively. This

figure indicates that both analysis and simulation results are consistent.

In the following, we investigate the PI,d and PA,d

perfor-mances for the Partition, CDC, and CDCQ schemes with the RR and Greedy algorithms based on the simulation models. In our study, the input parameters λI, λA, μI, δI, δA, and ts

are normalized by μA. For example, if the expected internal

packet transmission time is (1/μA) = 120 s, then λI = 6 μA

means that the expected external packet interarrival time is 20 s.

PI,d Performance for External Packets. Fig. 10 plots PI,d

as a function of λI/λI+ λA, where K = 4, M = 256, mI =

mA= 1, and μI = μA. Fig. 10(a) and (b) studies the effects

of α, where α = 60% and 90%. Fig. 10(a) and (c) investigates

Fig. 9. Comparison of the analytical and the simulation results for Partition_RR (K = 4; M = 256; mI= mA= 1; ts= 0).

the effects of scheduling period ts, where ts= μA (short

scheduling period), and ts= 10 μA (long scheduling period).

Fig. 10(a) and (d) evaluates the effects of queue delay boundary δI, where δI = μA (short delay boundary), and δI = 10 μA

(long delay boundary).

The general phenomena in Fig. 10 are described as follows: The PI,d values increase as λI/λI+ λA increases for all

schemes. This is because more external packets arrive during a period for larger λI/λI+ λAsetup, and they compete for the

minislots. All schemes with the Greedy algorithm outperform those with the RR algorithm due to the minislot reuse property. Furthermore, the CDC-series schemes outperform the Partition-series schemes in terms of PI,d performance. In the

CDC-series schemes, there is no partition boundary. The minislots are allocated to the external packets first (i.e., centralized schedul-ing is executed), and the remainschedul-ing minislots are allocated to the internal packets (i.e., distributed scheduling is exercised). Therefore, we observe that the CDC-series schemes gain better PI,dperformance for the external packets. We also observe that

the queuing mechanism (i.e., the IQ queue) does not improve the PI,dperformance. To summarize, CDC_Greedy (either with

or without the IQ queue) has the best PI,dperformance among

the six schemes.

1) Base Case: In Fig. 10(a), where α = 60%, the PI,dvalues

for Partition_Greedy, CDC_Greedy, and CDCQ_Greedy slightly increase and then rapidly increase as λI/λI+ λA

increases. For example, PI,d for CDC_Greedy slightly

increases as (λI/λI + λA)≤ 0.5 and then rapidly

in-creases as (λI/λI+ λA) > 0.5. The minislot allocation

for the external packets is exercised at the beginning of the scheduling period, and all external packet re-quests that arrive during the current scheduling period are buffered before they are processed in the next scheduling period. The external packets are batch arrivals. Conse-quently, if the number of arrivals during a scheduling period is less than the system capacity, then these arrivals can be served, and PI,dapproaches 0. On the other hand,

if the number of arrivals during a scheduling period is larger than the system capacity, these requests are more likely to compete for minislots, and the PI,dperformance

drops fast.

2) Effects of α: In Fig. 10(b), we increase α to 90%. The figure indicates that the PI,d performance for the

Fig. 10. Comparison for the PI,dperformance (K = 4; M = 256; mI= mA= 1; μI= μA). (a) α = 60%; λI+ λA= 10 μA; ts= μA; δI= δA=

μA. (b) α = 90%; λI+ λA= 10 μA; ts= μA; δI= δA= μA. (c) α = 60%; λI+ λA= 20 μA; ts= μA; δI= δA= μA. (d) α = 60%; λI+ λA=

10 μA; ts= 10 μA; δI= δA= μA. (e) α = 60%; λI+ λA= 10 μA; ts= μA; δI= 10 μA; δA= μA.

Partition-series schemes approximates that for the CDC-series schemes. This phenomenon is explained as follows: The Partition-series and CDC-series schemes allocate minislots for external packets first. Furthermore, as men-tioned in Section II, all minislots are reallocated at the beginning of the scheduling period. Therefore, as α in-creases, the number of minislots (that can be allocated to external packet arrivals) in the Partition-series schemes approaches that in the CDC-series schemes.

3) Effects of Total Traffic: In Fig. 10(c), we increase the total traffic to λI+ λA= 20 μA, and the PI,d performance

for the six schemes becomes worse. In this case, more external packets arrive during a scheduling period; these arrivals compete for minislots, and the worse PI,d

perfor-mance is observed.

4) Effects of ts: In Fig. 10(d), the length of the scheduling

period (i.e., ts) is ten times that in Fig. 10(a). With

larger ts, we may have two facts: 1) More external packet

requests arrive in a scheduling period. 2) It is more likely that an external packet completes during a scheduling period, and the minislots for the external packet may be idle until the next scheduling period, which results in poor

minislot utilization. The two aforementioned facts cause the PI,d performance to drop fast for both the

Partition-series and CDC-Partition-series schemes.

5) Effects of δI: In Fig. 10(e), we increase the queue

de-lay boundary δI for CDCQ_RR and CDCQ_Greedy ten

times that in Fig. 10(a). Compare the “×” and “” curves in Fig. 10(a) and (e); we observe that increasing δI

does not significantly improve the PI,dperformance. This

phenomenon guides us that it is not worth providing long delay boundary for the external packets.

PA,d Performance for Internal Packets: Fig. 11 plots PA,d

as a function of λI/λI+ λA, where K = 4, M = 256, mI =

mA= 1, and μI = μA. Like Fig. 10, Fig. 11 shows the effects

of α, the total traffic, scheduling period ts, and queue delay

boundary δA.

1) Base Case: Consider Fig. 11(a), where α = 60%. In this figure, the PA,d values for Partition_RR and Partition_

Greedy are zero and are not affected by λI/λI+ λA.

For the Partition-series schemes, the number of minis-lots reserved for internal packets is(1 − α)M = 103, and the internal traffic load is (λA/μA) = 9. There are

Fig. 11. Comparison for the PA,dperformance (K = 4; M = 256; mI= mA= 1; μI= μA). (a) α = 60%; λI+ λA= 10 μA; ts= μA; δI= δA=

μA. (b) α = 90%; λI+ λA= 10 μA; ts= μA; δI= δA= μA. (c) α = 60%; λI+ λA= 20 μA; ts= μA; δI= δA= μA. (d) α = 60%; λI+ λA=

10 μA; ts= 10 μA; δI= δA= μA. (e) α = 60%; λI+ λA= 10 μA; ts= μA; δI= μA; δA= 10 μA.

sufficient minislots that can serve internal packets. The PA,dvalues for CDC_RR and CDCQ_RR approach zero.

This is because, with the RR algorithm, CDC_RR and CDCQ_RR cannot reutilize the minislots to serve ex-ternal packets, and more minislots can serve inex-ternal packets.

For CDC_Greedy and CDCQ_Greedy, when (λI/λI +

λA) < 0.4, PA,d is 0; when 0.4 < (λI/λI+ λA) <

0.6, PA,d rapidly increases; and when (λI/λI+ λA) >

0.6, PA,d approaches 10%. With the Greedy

algo-rithm, CDC_Greedy and CDCQ_Greedy enable the minislot reuse for centralized scheduling, and two facts hold.

Fact 1) The minislots have more chance to be fully uti-lized for centrauti-lized scheduling.

Consider Fig. 7. In the WMN topology, the mesh BS is located at the center. All external packets should be routed through the layer-1 SSs. Thus, we have the following fact:

Fact 2) When λI/λI+ λAincreases, the minislots of the

layer-1 SSs are more likely to be occupied by external packets.

Due to Facts 1 and 2, in CDC_Greedy and CDCQ_Greedy, internal packet requests to the layer-1 SSs are more likely to be dropped. The PA,dvalues for CDC_Greedy and CDCQ_

Greedy are bounded by 10%. The total number of internal packet arrivals in all SSs is ten times that in layer-1 SSs (see Fig. 7).

2) Effects of α: In Fig. 11(b), we increase α to 90%. This figure indicates that α does not affect the PA,d

per-formance for CDC_RR, CDC_Greedy, CDCQ_RR, and CDCQ_Greedy. With the Partition-series schemes, the number of minislots reserved for internal packet arrival is (1 − α)M = 26. In this figure, we set λI + λA=

10 μA. When (λI/λI+ λA) = 0.1, the internal traffic

load is (λA/μA) = 9, and there are insufficient minislots

to serve the new internal packet arrivals. Therefore, we observe that, when (λI/λI+ λA) = 0.1, the PA,dvalue

for the Partition-series scheme is high (i.e., 20.3%). As λI/λI + λAincreases, the internal traffic load decreases.

Fewer internal packet requests arrive in a short period, and thus, the PA,dvalues decrease and approach zero.

3) Effects of Total Traffic: In Fig. 11(c), we increase the total traffic λI+ λA to 20 μA. We observe a similar

phenomena as in Fig. 11(a).

4) Effects of ts: In Fig. 11(d), the length of the scheduling

period is ten times that in Fig. 11(a). With a larger ts

setup, more external packet requests arrive in a schedul-ing period, fewer minislots can be allocated to internal packets, and the PA,dperformance for CDC_Greedy and

Fig. 12. Effects of the variances of external and internal packet interarrival times and transmission times (CDCQ_Greedy, K = 4, M = 256, α = 60%,

mI= mA= 1, μI= μA, ts= μA, δI= δA= μA). (a) and (b) Gamma-distributed external packet interarrival times. (c) and (d) Gamma-distributed internal

packet interarrival times. (e) and (f) Gamma-distributed external packet transmission times. (g) and (h) Gamma-distributed internal packet transmission times. 5) Effects of δA: In Fig. 11(e), we increase the queue delay

boundary δA for CDCQ_RR and CDCQ_Greedy to be

ten times that in Fig. 11(a). Compare the “” curves in Fig. 11(a) and (e); we observe that increasing δA does

not significantly improve the PA,d performance. This

phenomenon guides us that it is not worth providing a long delay boundary for the internal packets.

Effects of the Variations of the Distributions for Packet Input Parameters: In the following, we study the effects of the variances for external and internal packet interarrival/ transmission time distributions in the CDCQ_Greedy scheme. We set the interarrival times and transmission times for ex-ternal (inex-ternal) packets to have Gamma distributions with means 1/λI(1/λA) and 1/μI(1/μA) and variances vλI =

(1/α1λ2I)(vλA = (1/α2λ 2

A)) and vμI = (1/α3 μ 2

I)(vμA =

(1/α4 μ2A)), respectively, where α1, α2, α3, and α4> 0 are

shape parameters. Gamma distributions are considered, because they can be used to approximate many other distributions [16]– [19], [26]. Fig. 12 plots PI,dand PA,das functions of λI/λI+

λA, where K = 4, M = 256, α = 60%, mI = mA= 1, μI =

μA, ts= μA, and δI = δA= μA. To investigate the impacts of

variance for one input parameter, the distributions for the other

parameters are set to be exponential (i.e., the shape parameters are set to one).

1) Variance of External Packet Interarrival Time: Con-sider Fig. 12(a) and (b). Fig. 12(a) indicates that the PI,dperformance when vλI > (1/λ

2

I) is worse than that

that when vλI ≤ (1/λ 2

I). For the PA,d performance,

Fig. 12(b) indicates that, when (λI/λI + λA)≤ 0.5, the

PA,d values increase as vλI increases. When (λI/λI+

λA) > 0.5, the PA,d values decrease as vλI increases.

CDCQ_Greedy gains better performance when vλI ≤

(1/λ2

I).

2) Variance of Internal Packet Interarrival Time: Consider Fig. 12(c) and (d). Fig. 12(c) shows that PI,d is not

affected by vλA. In Fig. 12(d), we observe that the PA,d

performance is slightly affected by vλA.

3) Variance of External Packet Transmission Time: Fig. 12(e) and (f) indicates that both PI,d and PA,d

increase as vμI increases. We have better performance

for CDCQ_Greedy when vμI < (1/μ 2

I).

4) Variance of Internal Packet Transmission Time: From Fig. 12(g) and (h), we observe that PI,d is not

vμA increases. CDCQ_Greedy performs better when

vμA> (1/μ 2

A).

IV. CONCLUSION

This paper has proposed the CDC and CDCQ schemes to combine distributed scheduling and centralized scheduling in the IEEE 802.16 Standard. We expect that this will flexibly allocate the minislots in a data subframe to serve the external and internal packets in the WMN, whereas the IEEE 802.16 Standard proposed the Partition scheme for minislot allocation for two kinds of traffic packets. We conducted an analytical model and simulation experiments to investigate the perfor-mance for the Partition, CDC, and CDCQ schemes, where we used the RR and Greedy algorithms as baseline algorithms for the centralized scheduling. Our study indicates that the CDC scheme increases the external packet acceptance rate, and the queuing mechanism slightly reduces the dropping probability for external packet requests.

In terms of internal packet performance, this paper indicated that, for the CDC-series schemes with Greedy algorithm, the internal packet request dropping probability is bounded by the ratio of the number of SSs around the mesh BS over the total number of SSs in the WMN. Our study also indicates that the CDC-series schemes with RR algorithm outperform other schemes.

Finally, we investigated the performance of the variances of the external and internal packet interarrival times and transmis-sion times for the CDCQ scheme. Our study concluded that the CDC-series scheme increases the external and internal packet acceptance rates in all cases.

APPENDIXI

RRANDGREEDYALGORITHMS

This section describes the scheduling algorithms, i.e., RR and Greedy, adopted in the second stage of a scheduling period. The scheduling algorithm has two purposes: 1) to calculate the number of external packet requests (from SSai)

that can be served by the WMN and 2) to determine the minislots that can serve an external packet request. Let (au, av)

denote the wireless link between SSau and SSav, and let E

be the set containing the wireless links among the SSs and the mesh BS. The operation GET(ai, j) gets the status of

the jth minislot from Sai, and SET(ai, j,{TX, RX, F}) sets the

status of the jth minislot serving for SSai. Suppose that the

WMN consists of N SSs with the scheduling tree T = {a0(ka0, na0), a1(ka1, na1), a2(ka2, na2), . . . , aN(kaN, naN)},

where kai is the layer number, nai is the position number in

layer kai, and (kai, nai) is called the index number of the SS.

Without loss of generality, the index number of the mesh BS is (0, 0). Fig. 1(b) shows an example for the scheduling tree for Fig. 1(a). In the two scheduling algorithms, we maintain an array Aaifor SSaito store the node IDs of the mesh BS and the

SSs on the routing path from the mesh BS to SSaiin increasing

order of their layer numbers. Assume that there are raiexternal

packet requests arriving at SSai during a scheduling period,

and each packet requests mI,aiminislots for data transmission.

Fig. 13. Pseudocode for the RR algorithm.

The scheduling algorithm is executed to calculate the number r_ai of accepted external packet requests for SSai. Initially,

the statuses of all minislots are set as F. The RR and Greedy algorithms function as follows.

A. Algorithm RR

Fig. 13 shows the pseudocodes for the RR algorithm. The scheduling algorithm outputs a variable rai(i.e., the number of

granted external packet requests for SSai) and status array Sai

for SSai. The RR algorithm does not adopt the minislot reuse

property in TDM, and each minislot is allocated to at most one SS. At line 1 of Fig. 13, using the scheduling tree, the mesh BS sorts the node IDs of the SSs in increasing order of their layer numbers and generates an ordered list L =a₁, a₂, a₃, . . . , a_N such that ka1 ≤ ka2≤ · · · ≤ kaN. At line 2, the variable j is

used to indicate the current minislot of the algorithm processes. Initially, j is set to 1. At lines 3–13, a for loop is executed to set the status of the minislots for each SS, following the order in the L list. Line 4 initializes r_a

i as zero. Line 5 checks whether

rai > 0 and mI,ai> 0. If rai = 0 or mI,ai = 0 (i.e., SSaidoes

not request any minislot for data transmission), the mesh BS skips the minislot reservation for SSa_i. Otherwise, lines 6–13

execute a for loop to reserve minislots for each external packet request that arrives in SSa_i. Lines 7–12 execute two for loops

to reserve mI,a_i minislots for each SS in Aa_i. Line 9 sets the

jth minislots as TX for SSA_a

i[p]

(p is the index number in Aai, i.e., the minislot is reserved for data transmission) and

sets the jth minislot as RX for SSAa i[p−1]

(i.e., the minislot is reserved for data reception). Line 10 increases j by 1. Line 11 checks whether j = 256. If so (i.e., there are insufficient minislots), the algorithm quits at line 12. As all SSs in Aai

successfully reserve mI,ai minislots for data transmission,

line 13 increases r_a

i by 1, which implies that the request is

accepted.

B. Algorithm Greedy

Fig. 14 shows the pseudocodes for the Greedy algorithm. The Greedy algorithm is similar to the RR algorithm; however, in

Fig. 14. Pseudocode for the Greedy algorithm.

the Greedy algorithm, we adopt the minislot reuse technology. In this algorithm, we implement the Collision function to determine whether the allocation of the jth minislot to SSau

for transmitting data to its neighbor SSav will cause a collision,

which is shown here. COLLISION (au, av, j)

if GET(au, j)= F or GET(av, j)= F then

return TRUE fori← 1 to N do

if [(ai, au)∈ E and GET(ai, j) = RX] or [(ai, av)∈ E

and GET(ai, j) = TX] then

return TRUE return FALSE

The Greedy algorithm is similar to the RR algorithm. The difference is that the mesh BS performs the COLLISION function to find a minislot with the smallest index and then allocates the minislot to SSAa

i[p]

and SSAa i[p−1]

.

APPENDIXII

STATETRANSITIONS FOR THECENTRALIZED SCHEDULINGMARKOVPROCESS IN

PARTITION_RRANDCDC_RR

Fig. 8 shows the state transition diagram for the Markov process. In this figure, we consider the transitions for state (w, x, y, z)∈ S given here.

• If an external packet arrives in a layer-1 SS when the process is at state (w, x, y, z)∈ S, where w + 2x + 3y + 4z≤ αM/mI − 1, then one minislot is allocated.

Define δ+₁ as δ₁+=  1, if w + 2x + 3y + 4z≤  αM mI  − 1 0, otherwise. (7)

The process moves from state (w, x, y, z) to (w + 1, x, y, z) with rate 3λIδ+1 since there are three

layer-1 SSs.

• If the transmission for an external packet completes when the process is at state (w + 1, x, y, z)∈ S, two minislots will be released. The process moves from state (w + 1, x, y, z) to (w, x, y, z) with rate (w + 1)μIδ2+, where

δ₂+= 

1, if (w + 1, x, y, z)∈ S

0, otherwise. (8)

• If an external packet arrives in a layer-2 SS when the process is at state (w, x, y, z)∈ S, where w + 2x + 3y + 4z ≤ αM/mI − 2, then two minislots are allocated.

Define δ+₃ as δ₃+=  1, if w + 2x + 3y + 4z≤  αM mI  − 2 0, otherwise. (9)

The process moves from state (w, x, y, z) to (w, x + 1, y, z) with rate 6λIδ3+since there are six layer-2 SSs.

• If the transmission for an external packet is completed when the process is at state (w, x + 1, y, z)∈ S, four minislots will be released. The process moves from state (w, x + 1, y, z) to (w, x, y, z) with rate (x + 1)μIδ+4, where δ₄+=  1, if (w, x + 1, y, z)∈ S 0, otherwise. (10)

• If an external packet arrives in a layer-3 SS when the process is at state (w, x, y, z)∈ S, where w + 2x + 3y + 4z ≤ αM/mI − 3, then three minislots are allocated.

Define δ+₅ as δ+₅ =  1, if w + 2x + 3y + 4z≤  αM mI  − 3 0, otherwise. (11)

The process moves from state (w, x, y, z) to (w, x, y + 1, z) with rate 9λIδ5+since there are nine layer-3 SSs.

• If the transmission for an external packet completes when the process is at state (w, x, y + 1, z)∈ S, six minislots will be released. The process moves from state (w, x, y + 1, z) to (w, x, y, z) with rate (y + 1)μIδ+6, where

δ₆+= 

1, if (w, x, y + 1, z)∈ S

0, otherwise. (12)

• If an external packet arrives from a layer-4 SS when the process is at state (w, x, y, z)∈ S, where w + 2x + 3y +

4z≤ αM/mI − 4, then four minislots are allocated. Define δ+₇ as δ₇+=  1, if w + 2x + 3y + 4z≤  αM mI  − 4 0, otherwise. (13)

The process moves from state (w, x, y, z) to (w, x, y, z + 1) with rate 12λIδ7+since there are 12 layer-4 SSs.

• If the transmission for an external packet completes when the process is at state (w, x, y, z + 1)∈ S, eight minislots will be released. The process moves from state (w, x, y, z + 1) to (w, x, y, z) with rate (z + 1)μIδ8+, where δ+₈ =  1, if (w, x, y, z + 1)∈ S 0, otherwise. (14)

The transitions between (w, x, y, z) and (w− 1, x, y, z), (w, x− 1, y, z), (w, x, y − 1, z), and (w, x, y, z − 1) are simi-lar to those between (w, x, y, z) and (w + 1, x, y, z), (w, x + 1, y, z), (w, x, y + 1, z), and (w, x, y, z + 1). The balance equa-tions for the Markov process are expressed in (5), where δ₁+, δ₂+, . . ., δ+₈ are obtained from (7)–(14), respectively, and

δ−₁ =  1, if (w− 1) + 2x + 3y + 4z ≤  αM mI  − 1 0, otherwise δ−₂ =  1, if (w− 1, x, y, z) ∈ S 0, otherwise δ−₃ =  1, if w + 2(x− 1) + 3y + 4z ≤  αM mI  − 2 0, otherwise δ−₄ =  1, if (w, x− 1, y, z) ∈ S 0, otherwise δ−₅ =  1, if w + 2x + 3(y− 1) + 4z ≤  αM mI  − 3 0, otherwise δ−₆ =  1, if (w, x, y− 1, z) ∈ S 0, otherwise δ−₇ =  1, if w + 2x + 3y + 4(z− 1) ≤  αM mI  − 4 0, otherwise δ−₈ =  1, if (w, x, y, z− 1) ∈ S 0, otherwise. ACKNOWLEDGMENT

The authors would like to thank the editor and the three anonymous reviewers for their valuable comments and their efforts, which have significantly improved the quality of this paper.

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Mohsen Guizani (S’87–M’90–SM’98) received the

B.S. (with distinction) and M.S. degrees in elec-trical engineering and the M.S. and Ph.D. degrees in computer engineering from Syracuse University, Syracuse, NY, in 1984, 1986, 1987, and 1990, respectively.

He is currently a Professor and the Chair of the Department of Computer Science, Western Michigan University, Kalamazoo. He currently serves on the editorial boards of six technical journals and is the Founder and Editor-in-Chief of Wireless

Commu-nications and Mobile Computing Journal (Wiley, http://www.interscience.

wiley.com/jpages/1530-8669/) and the Journal of Computer Systems, Networks

and Communications, (Hindawi, http://www.hindawi.com/journals/).He is the

author of six books and more than 200 publications in refereed journals and conference proceedings. His research interests include computer networks, wireless communications and mobile computing, and optical networking.

Dr. Guizani is an active member of the IEEE Communication Society, the IEEE Computer Society, the American Society for Engineering Education, and the Association for Computing Machinery. He is the past Chair of TAOS and the Vice-Chair of WTC IEEE ComSoc Technical Committees. He has been a Guest Editor for a number of special issues of IEEE journals and magazines. He has also served as a member, Chair, and General Chair of a number of conferences. He is also the Founder and General Chair of the IEEE International Conference of Wireless Networks, Communications, and Mobile Computing (IEEE WirelessCom 2005, 2006, 2007, and 2008). He was the recipient of both the Best Teaching Award and the Excellence in Research Award from the University of Missouri, Columbia, in 1999 (a college-wide competition); the Best Research Award from the King Fahd University of Petroleum and Minerals in 1995 (a university-wide competition); and the Best Teaching Assistant for two consecutive years at Syracuse University in 1988 and 1989.

Phone Lin (M’02–SM’06) received the BSCSIE

and Ph.D. degrees from National Chiao Tung Uni-versity, Hsinchu, Taiwan, R.O.C., in 1996 and 2001, respectively.

From August 2001 to July 2004, he was an Assistant Professor with the Department of Com-puter Science and Information Engineering (CSIE), National Taiwan University, Taipei, Taiwan. Since August 2004, he has been an Associate Professor with the Department of CSIE and the Graduate Insti-tute of Networking and Multimedia, National Taiwan University. His current research interests include personal communications services, wireless Internet, and performance modeling. He has published more than 20 international SCI journal papers (most of which are IEEE TRANSACTIONSand ACM papers).

Dr. Lin is an Associate Editor of the IEEE TRANSACTIONS ONVEHICULAR TECHNOLOGY, a Guest Editor for IEEE Wireless Communications special issue on Mobility and Resource Management, and a Guest Editor for

ACM/Springer MONET special issue on Wireless Broad Access. He is also an

Associate Editorial Member for the WCMC Journal. He has received many research awards. He was elected as the Best Young Researcher at the 3rd IEEE ComSoc Asia-Pacific Young Researcher Awards in 2007. He was a recipient of the Research Award for Young Researchers from the Pan Wen-Yuan Foundation in Taiwan in 2004, a recipient of the K. T. Li Young Researcher Award from the ACM Taipei Chapter in 2004, a recipient of the Wu Ta You Memorial Award of the National Science Council (NSC) in Taiwan in 2005, a recipient of the Fu Suu-Nien Award of NTU in 2005 for his research achievements, and a recipient of the 2006 Young Electrical Engineering Award of the Chinese Institute of Electrical Engineering. Dr. Lin was listed in Who’s Who in Science

and Engineeering in 2006.

Shin-Ming Cheng (M’06) received the B.S. and

Ph.D. degrees in computer science and informa-tion engineering from Nainforma-tional Taiwan Univer-sity, Taipei, Taiwan, R.O.C., in 2000 and 2007, respectively.

He is currently a Postdoctoral Researcher with the Department of Electrical Engineering, National Taiwan University. His research interests include mobile networking, wireless communications, and network security.

Di-Wei Huang received the B.S. degree in computer

science and information engineering from National Chiao Tung University, Hsinchu, Taiwan, R.O.C., in 2004 and the M.S. degree in computer science and information engineering from National Taiwan University, Taipei, Taiwan, in 2006.

During 2006–2007, he was on active duty of obligatory military service in Taiwan. He is currently with the Department of Computer Science and Infor-mation Engineering, National Taiwan University. His current research interests include wireless network-ing and mobile computnetwork-ing.

Huai-Lei Fu received the B.S. degree in computer

science from Tatung University, Taipei, Taiwan, R.O.C., in 2005 and the M.S. degree in computer science from Yuan Ze University, Taoyuan, Taiwan, in 2007. He is currently working toward the Ph.D. degree in computer science with the Department of Computer Science and Information Engineering, National Taiwan University, Taipei.

His research interests include wireless commu-nication, wireless mesh networks, and peer-to-peer streaming.