Overview of the PRP M/G/1 Queueing Network Model 37

Now we propose a preemptive resume priority (PRP) M/G/1 queueing net-work model to characterize the connection-based spectrum usage behaviors in CR networks. This queueing network analytical framework is quite general and can be easily adjusted to evaluate the performance of various spectrum management techniques under different traffic conditions. Furthermore, it can also be applied to general CR network architectures, including ad hoc

CR network and centralized CR networks such as the IEEE 802.22 standard.

Key features of the proposed PRP M/G/1 queueing network model are listed below:

• Each server (channel) has two types of customers (connections). Before transmitting data, the traffic of the primary and the secondary users en-ter to the high-priority queue and the low-priority queue², respectively.

Then, according to the traffic arrival time at queues, the primary con-nections and the secondary concon-nections can be established without any collision. Here, we assume that the connections with the same priority follow the first-come-first-served (FCFS) scheduling discipline³.

• The primary users have the preemptive priority to interrupt the trans-mission of the secondary users. The interrupted secondary user can resume the unfinished transmission on the selected target channel, in-stead of retransmitting the whole data. Note that the target channel of an interrupted secondary connection can be different from its current operating channel. This is a key difference from the spectrum usage model based on the conventional PRP M/G/1 queueing theory [16–18].

• A secondary connection may experience multiple interruptions from the primary users during its transmission period. This model can charac-terize the effects of multiple spectrum handoffs.

Note that this model can be also extended to characterize the effects of sensing errors (i.e., missed detection and false alarm) and the heterogeneous

2Note that we assume the considered two queues have an infinite length.

3In fact, the analytical results of mean values obtained based the proposed framework can be applied to other scheduling discipline which is independent of the service time of the primary and secondary connections because the averages of system performance metrics will be invariant to the order of service in this case (see page 113 in [78]).

High-priority

Figure 3.2: The PRP M/G/1 queueing network model with three channels.

λ^(k)p , λ^(k)s , and ωn^(k) are the arrival rates of the primary connections, the sec-ondary connections, and the type-n secsec-ondary connections (n ≥ 1) at channel k. Note that ω₀^(k) = λ^(k)s . Furthermore, fp^(k)(x) and f_i^(k)(φ) are the pmfs of Xp^(k) and Φ^(k)_i , respectively.

channel bandwidth [79]. Some assumptions are adopted for ease of analysis.

• The arrival processes of the primary and the secondary connections are Poisson.

• Only one user can transmit on each channel at any time instant.

• The secondary transmitter can notifies its corresponding receiver of the interruption event by certain spectrum handoff protocols [80].

Figure 3.2 shows an example of the PRP M/G/1 queueing network model with three channels. Let λ_s (arrivals/slot) be the arrival rates of the sec-ondary connections in CR network. When a secsec-ondary connection arrives

at CR network, it can select its initial operating channel from one of three channels. Let p^(k)be the probability that it selects channel k for its initial op-erating channel. Thus, the effective arrival rate of the secondary connection at channel k is λ^(k)s = p^(k)λs. Note that various spectrum decision algorithms will yield different values of p^(k).

When a newly arriving secondary connection is connected to the low-priority of its initial operating channel, it can be transmitted immediately if the selected channel is idle. Otherwise, it must wait until this channel becomes idle. Furthermore, when a secondary connection is transmitting at channel k, it will be interrupted if a primary user appears at channel k. In this case, the secondary connection can either stay on the current operating channel or change to another channel through different feedback paths. The decision depends on which operating mode and spectrum handoff scheme are adopted. If the secondary connection chooses to stay on its current operating channel, the remaining data of the interrupted secondary connection must wait at the head of the low-priority queue of the current operating channel.

If the decision is to change its operating channel, its remaining data will be connected to the tail of the low-priority queue of another channel. Note that ⊕ represents that the traffic of the interrupted secondary connection is merged. Furthermore, when the interrupted secondary connection transmits its remaining data on the selected target channel, it may be interrupted again. Hence, this model can describe the effects of multiple handoffs.

In Fig. 3.2, S represents the channel selection point, where the newly arriving secondary connection must select its initial operating channel or the interrupted secondary connection must select its target channel for spectrum handoff. There are many methods to select these channels. For example, the secondary connection can decide its initial operating channel or target

channel according to the predetermined probability or the outcomes from in-stantaneous spectrum sensing. If the spectrum sensing is executed to search the idle channels, S can be regarded as a tapped delay line or a server with constant service time, which related to sensing time. Hence, the ef-fect of spectrum sensing time on the latency performance of the secondary connections can be characterized.

3.3.3 Modeling of the Connection-based Channel Us-age Behaviors

Now, we explain why the proposed model can characterize the connection-based channel usage behaviors in a CR network. In order to accurately characterize the transmission processes of a secondary connection, we must take the seven events as discussed in Section 3.2 into account.

1. Secondary connection arrival event as shown in Fig. 3.1(a): We assume that the arrival process of the secondary connections is Poisson. Let X_s be the service time of the secondary connections and f_s(x) be the probability mass function (pmf) of X_s.

2. Initial channel selection event of the secondary connections as shown in Fig. 3.1(b): We use p^(k) to represent the probability that the sec-ondary connection selects channel k for its initial operating channel.

Furthermore, if the spectrum sensing is executed to decide the initial operating channel, the effect of sensing time can be modeled by S . 3. Primary connection arrival event as shown in Fig. 3.1(c): We assume

that the arrival process of the primary connections is Poisson. Denote λ^(k)p as the arrival rate of the primary connections whose default chan-nels are channel k. Furthermore, let X^(k) be the service time of the

primary connections whose default channels are channel k and fp^(k)(x) be the pmf of Xp^(k).

4. Interruption event as shown in Fig. 3.1(d): In the PRP M/G/1 queue-ing network model, the primary users have the preemptive priority and thus they can interrupt transmission of the secondary users. In other words, the secondary users must vacate the occupied channel when the primary users appear.

5. Target channel selection event as shown in Fig. 3.1(e): An interrupted secondary connection can either stay on its current channel or change to another channel. To this end, its remaining transmission must be con-nected to the low-priority queue of current channel or another channel through different feedback paths. Furthermore, if the spectrum sensing is executed to search the target channel, the effect of sensing time can be modeled by S .

6. Resumption event as shown in Figs. 3.1(f)-(h): The interrupted sec-ondary connection can resume its unfinished transmission on the target channel, instead of retransmitting the whole data.

7. Multiple handoff events: Two auxiliary parameters (ω^(k)_i and Φ^(k)_i ) are suggested to characterize the traffic flows of the interrupted secondary connections.

3.3.4 Two Auxiliary Parameters: ω

_i^(k)

and Φ

^(k)_i

In Fig. 3.2, we use two auxiliary parameters to characterize the traffic flows of the interrupted secondary connections. We call the secondary tions which have experienced i interruptions the type-i secondary

connec-tions where i ≥ 0. At channel k, denote ω_i^(k) as the arrival rate of traffic flows redirected from the type-(i − 1) secondary connections. That is, ω_i^(k) is the arrival rate of the type-i secondary connections at channel k. Note that ω^(k)₀ = λ^(k)s . Furthermore, let Φ^(k)_i be the transmission duration of a sec-ondary connection between the i^th and the (i + 1)^th interruptions at channel k and f_i^(k)(φ) be the pmf of Φ^(k)_i . That is, Φ^(k)_i is the effective service time of the type-i secondary connections at channel k.

Figure 3.3 illustrates the physical meaning of random variable Φ^(k)_i . Recall that X_sis the service time of the secondary connections. We generate X_sfive times in Fig. 3.3. The five realizations are divided into many segments due to multiple primary users’ interruptions. For example, the first secondary connection (realization) is divided into four segments because it experiences three interruptions in total. The first, second, third, and fourth segments are transmitted at channels 1, 1, 1, and 2, respectively. Thus, this secondary connection’s initial operating channel is Ch1 and its target channel sequence is (Ch1,Ch1,Ch2). In Fig. 3.3, random variable Φ⁽¹⁾₂ is one of the gray regions, representing the transmission duration of a secondary connection between the 2^nd and the 3^rd interruptions at Ch1. That is, Φ⁽¹⁾₂ is one of the third segments of the first, the third, and the fourth secondary connections in Fig. 3.3. Note that the fifth secondary connection in Fig. 3.3 does not have the third segment because it is interrupted only once.

In the hopping mode, it is quite complex to find the probability mass function of the effective service time of each segment because the effective service time is dependent on the traffic statistics of the primary and other sec-ondary users of each channels and the operating channels for these segments can be different. Fortunately, based on the proposed analytical framework, we provide a systematic approach to study the effects of various system

pa-rameters on the effective service time and then can derive the closed-from expression for the probability mass function of the effective service time of each segment.

3.3.5 Constraint

Finally, we denote ρ^(k)as the busy probability of channel k. In an M-channel network, the following constraint shall be satisfied:

ρ^(k), λ^(k)_p E[X_p^(k)] + X∞

i=0

ω_i^(k)E[Φ^(k)_i ] < 1 , (3.1)

Note that ρ^(k) can be also interpreted as the utilization factor of channel k.

3.4 Summary

In the following chapters, we will discuss various spectrum management tech-niques to demonstrate the effectiveness of this analytical model. For the spec-trum decision issue, we show how to determine which channels are required to probe and transmit. For the spectrum mobility issue, we illustrate how to characterize the effects of multiple handoffs, where the secondary users can have different operating channels before and after spectrum handoff. For the spectrum sharing issue, we explore how to determine the optimal admission probability to avoid the interference between primary and secondary users in the presence of false alarm and missed detection.

#2 on Ch2 #4 on Ch1

#2 on Ch1 #4 on Ch2

#1 on Ch1

#1 on Ch2 #2 on Ch1

#1 on Ch2 #2 on Ch1 #3 on Ch1 #4 on Ch2

#1 on Ch2 #2 on Ch2

#3 on Ch2

#5 on Ch1

1st 2nd 3rd

1st 2nd

2nd

1st

3rd 4th

1st

Interruption Event Occurs

#1 on Ch1

1st 2nd 3rd

#3 on Ch1

#3 on Ch1

Figure 3.3: Illustration of the physical meaning of random variable Φ^(k)_i . For example, Φ⁽¹⁾₂ is one of the third segments (gray areas) of the first, the third, and the fourth secondary connections.

Chapter 4

Load-Balancing Spectrum Decision

Spectrum decision is a crucial process in CR networks [13], which helps the secondary user select the best channel to transmit data from candidate chan-nels. In order to distribute the traffic loads of the secondary users evenly to these candidate channels, an effective spectrum decision scheme should take the traffic statistics of the primary users as well as the secondary users into account. In this chapter, we introduce a performance measure for evaluating various spectrum decision schemes – the overall system time of the secondary connection, which is defined as the duration from the instant that data arrives at system until the instant of finishing the whole transmission.

In this chapter, we investigate how to evaluate the overall system time for the sensing-based and the probability-based spectrum decision schemes in the CR network when multiple interruptions from the primary user and sensing errors are taken into account. To this end, we design our multiuser spectrum decision schemes on top of the preemptive resume priority (PRP) M/G/1 queueing model. Based on the proposed analysis-based framework,

we can design the suitable parameters to shorten the overall system time.

Unlike the non-load-balancing methods that multiple secondary users may contend for the same channel, the channel selection schemes based on the designed parameters of the proposed analytical model can evenly distribute the traffic loads of secondary users to multiple channels, thereby reducing the average overall system time. The major contributions of this chapter are summarized in the following:

• Derive the optimal selection probability for the probability-based chan-nel selection scheme.

• Develop a method to determine the optimal number of candidate chan-nels for the sensing-based channel selection scheme.

• Compare the sensing-based and the probability-based channel selection methods and suggest which spectrum decision scheme can result in shorter overall system time with various sensing error probabilities and traffic parameters.

• Characterize the effects of sensing errors on the spectrum decision schemes of CR networks in terms of the overall system time of the primary and the secondary connections.

4.1 Motivation

The overall system time of the secondary users’ connections is affected by the multiple interruptions from the primary users and the sensing errors like missed detection and false alarm for the primary users. Within the transmission period of the secondary users’ connection, it is likely to have multiple spectrum handoffs due to the interruptions from the primary users.

Clearly, multiple spectrum handoffs will increase the overall system time [71].

In the meanwhile, false alarm occurs when the detector mistakenly reports the presence of a primary user. In this situation, the overall system time of the secondary user’s connections becomes longer because the secondary users cannot transmit data even with an idle channel. When the detection of a primary user is missed, data collision of both the primary user and the secondary user occurs, resulting in retransmitting and prolonging the overall system time of the secondary users’ connections. Hence, it is crucial is incorporating the effects of multiple handoffs and the sensing errors of false alarm and missed detection in spectrum decision methods for CR networks.

In this chapter, two kinds of spectrum decision schemes are considered:

(1) the sensing-based spectrum decision scheme; and (2) the probability-based channel selection scheme. For the sensing-probability-based spectrum decision method, a secondary user selects its operating channel according to the in-stantaneous sensing results from scanning the wideband spectrum. For the probability-based spectrum decision method, the operating channel is se-lected based on the predetermined probabilities which are determined ac-cording to traffic statistics from the long-term observation. Note that the sensing outcomes in both the methods are related to the traffic statistics of both the primary users and the secondary users. The two considered spec-trum decision schemes have different design issues. For the sensing-based spectrum decision scheme, the total number of candidate channels for chan-nel selection significantly affects the overall system time because this scheme requires scanning all the candidate channels. Intuitively, a narrowband sens-ing (or a smaller number of candidate channels) can reduce the total senssens-ing time. However, it is difficult to find one idle channel from a small number of candidate channels. Hence, one challenge is to determine the optimal

num-ber of candidate channels to minimize the overall system time. On the other hand, the probability-based spectrum decision scheme needs to prevent the secondary users from selecting a busy channel. Hence, the most important issue is to determine the optimal channel selection probability to minimize the overall system time.

4.2 System Model

4.2.1 Assumptions

In practice, many reasons may lead to an error on sensing the presence of the primary users. If such an sensing error occurs, not only the primary user’s connection will be stained, but the secondary user’s transmission will be affected. There are two types of sensing errors regarding the detection of the primary users: false alarm and missed detection. False alarm occurs when the detector reports the presence of a primary user while it is absent, while missed detection occurs when the detector reports the absence of a primary user while it is present. In this chapter, the effects of false alarm and missed detection on CR network performance are discussed in Section 4.5.

4.2.2 Spectrum Decision Behavior Model

Fig. 4.1 illustrates the spectrum decision behavior model, which will be used to evaluate the overall system time of a secondary user’s connection for dif-ferent channel selection schemes. We assume that the arrival processes of the primary and the secondary connections¹ are Poisson. Let λ^(k)p (arrivals/slot)

1When a secondary transmitter has data to send, how to establish a secondary connec-tion to its intended receiver has been investigated in [81].

Channel 1 with and

Channel 2 with and

Channel M with and

Channel Selection Algorithm

and

Figure 4.1: Spectrum decision behavior model.

and λ_s (arrivals/slot) be the average arrival rates of the primary connections at channel k and the secondary connections of CR network, respectively.

Also, denote Xp^(k) (slots/arrival) and X_s (slots/arrival) the service time of the primary connections of channel k and the secondary connections, respec-tively; and let fp^(k)(x) and f_s(x) be the probability mass functions (pmf) of Xp^(k) and X_s, respectively. It is assumed that λ^(k)p , λ_s, fp^(k)(x), and f_s(x), which can be estimated by the existing methods [82], are known to all the secondary users.

As shown in Fig. 4.1, each secondary connection can select one of M can-didate channels for its operating channel. Based on our proposed analytical framework, which will be discussed in more detail later, all the secondary users can dynamically select their operating channels with suitable probabil-ity that can balance the traffic loads of secondary users in multiple channels.

The distribution probability vector (denoted by p = (p⁽¹⁾, p⁽²⁾, · · · , p^{(M )})) represents the set of probabilities for selecting all the candidate channels, in which p^(k)denotes the probability of a secondary connection selecting channel

k for its operating channel. Thus, the effective arrival rate of the secondary connection at channel k is λ^(k)s = p^(k)λs. Note that various channel selection algorithms yield different distribution probability vectors.

4.3 Problem Formulation

4.3.1 Performance Metric: Overall System Time

The overall system time (denoted by S) is an important quality of service (QoS) metric for the connection-based service of the secondary users. It consists of the waiting time (denoted by W ) and the extended data delivery time (denoted by T ) as shown in Fig. 4.2. Hence, we have

E[S] = E[W ] + E[T ] , (4.1)

where E[·] is the expectation function. Here, the waiting time is defined as the duration from the instant that a data transmission request arrives at the system until the instant of starting transmitting data. The duration of waiting time depends on the channel selection scheme that the secondary users adopt. Furthermore, the extended data delivery time is defined as the duration from the beginning of transmitting the data in the first time slot until the completion of the data in the last time slot. Clearly, multiple handoff behaviors significantly affect the extended data delivery time.

4.3.2 Overall System Time Minimization Problem for Probability-based Channel Selection Scheme

For the probability-based channel selection method, each secondary user se-lects its operating channel from all the M candidate channels based on a

PCs PCs

W T

t

S

SC_A SC_A SC_A

Arrival of PC Spectrum Handoff

Arrival of SC

_A

Departure of SC

_A

Figure 4.2: Example of the overall system time of the secondary connection SC_A. The white areas indicate that channel is occupied by SC_A. Further-more, the gray areas indicate that channel is occupied by the primary connec-tions (PCs) and its duration is the busy period resulting from transmissions of the primary connections. Here, SCA encounters two interruptions from the primary connections during its transmission period.

predetermined distribution probability vector p_pb. In this case, an Overall

predetermined distribution probability vector p_pb. In this case, an Overall

在文檔中 以排隊理論為基礎對感知無線網路頻譜管理技術之研究 (頁 61-0)