HSDPA User Equipment Categories

An Integrated Analytical Model for Computation and Comparison of the Throughputs of the UMTS/HSDPA User Equipment Categories Tien Van Do Ram Chakka ...
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An Integrated Analytical Model for Computation and Comparison of the Throughputs of the UMTS/HSDPA User Equipment Categories Tien Van Do

Ram Chakka

Peter G. Harrison

Department of Telecommunications, Budapest University of Technology and Economics,

Meerut Institute of Engineering and Technology (MIET), Meerut 250005, India

Department of Computing, Imperial College, 180 Queen’s Gate, London, SW7 2BZ, UK

[email protected]

[email protected]

ABSTRACT A new queuing model is proposed for the performance evaluation of the High Speed Downlink Packet Access (HSDPA) protocol, with respect to a specified user, in UMTS networks. The model is based on the recently evolved P MM K CP Pk /GE/c/L G-queue1 , in which the number k=1 of servers allocated to a specified user is subjected to vary according to the physical channel allocation policy. This queue is, essentially, an important variant of the so-called Sigma queuing model, and it is able to capture most of the features of HSDPA wireless communications, such as trafficburstiness, channel fading, channel allocation policy, etc., in an integrated way. Numerical results for the performance of HSDPA with respect to a specified user are obtained, and different HSDPA user equipment categories are compared with respect to their computed model throughputs.

Categories and Subject Descriptors C.4 [Performance of Systems]: Modeling techniques

General Terms Performance

Keywords HSDPA Terminal Category, Performance Evaluation, Generalised Markovian Queue, MMCPP

1.

INTRODUCTION

The Universal Mobile Telecommunications System (UMTS) is one of the technologies standardised by the 1 MM – Markov Modulated, CPP – Compound Poisson Process

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[email protected]

International Telecommunications Union – Telecommunication Standardisation Sector (ITU-T) for third generation (3G) networks, with the aim to provide and support location-independent access to any service (voice, video and data). High Speed Downlink Packet Access (HSDPA) was introduced by the 3rd Generation Partnership Project (3GPP) to satisfy the demands for high speed data transfer in the downlink direction in UMTS networks. It can offer peak data rates of up to 10 Mbps, which is achieved essentially by the use of Adaptive Modulation and Coding (AMC), extensive multicode operation and a retransmission strategy [3]. However, efficient operation of HSDPA does require fast performance evaluation models in order to design, dimension, operate, maintain and update the system, costeffectively and efficiently. Such a performance model should be able to accommodate simultaneously all the important features and aspects pertaining to the operation of HSDPA, e.g., burstiness and the correlation amongst data traffic, channel assignments between voice and data traffic, channel coding schemes, as well as effects of the wireless environment such as channel fading. In the literature, most works have used simulation to evaluate the performance of HSDPA [4, 7, 10]. Liu et al. [9] and Yang et al. [14] were the first to consider the interaction between queuing at the data link layer and AMC at the physical layer, in an analytical model. However, their analysis assumed Poisson arrivals at the data link layer and did not explicitly account for HSDPA. Moreover, we are aware of no work to date that attempts to quantitatively compare HSDPA user equipment (UE) categories. This paper proposes a novel performance model for HSDPA in the data link layer. The new type of an introduced queue is able to capture various aspects concerning HSDPA wireless communications, such as traffic-burstiness, channel fading, channel allocation policy, etc., in an integrated way. That model is a generalised Markovian queue called PK the MM k=1 CP Pk /GE/c/L G- queue with the varying number of servers. The queue we consider consists of c homogeneous servers having independent and identically distributed Generalised Exponential (GE) service times and a buffer with either a finite or infinite size, i.e. with size L ≤ ∞. The arrivals are the superposition of K independent positive and one independent negative arrival streams, each one a Compound Poisson Process (CPP). In addition, and importantly, the arrival parameters, service parameters

and the parameter c are all modulated jointly by an external modulating continuous time Markov chain. cm is the maximum value of c. This is a very useful variant of the Sigma queuing model presented in [5, 6]. Numerical results evaluating the performance of HSDPA with respect to a specified (single) user are obtained along with some interesting figures that compare several user equipment (UE) categories, quantitatively. The rest of the paper is organised as follows. Section 2 provides an overview of HSDPA and section 3 describes our proposed model for it. Numerical results are presented and discussed in section 4 and the paper concludes in section 5.

2.

HSDPA OPERATION

A UMTS network consists of three interacting, autonomous domains: Core Network (CN), UMTS Terrestrial Radio Access Network (UTRAN) and User Equipment (UE) or a Subscriber Station (SS). In the UMTS UTRAN domain, the Radio Network Controller (RNC) manages a set of base stations (called Node-B’s) and is responsible for the radio resource control and management tasks related to the air interface. Node-B provides the radio interface for UEs. That is, Node B is responsible for the transmission and reception of data across the radio interface (that includes the interface to and from the UEs).

Uplink channels (HS-DPCCH, DCH) channel quality feedback Downlink channels HS-DSCH: user data HS-SCCH: control information

UE Node-B

Figure 1: Channels in HSDPA In the implementation of HSDPA, several channels are introduced (Fig. 1). The transport channel carrying the user data, in HSDPA operation, is called the High-Speed Downlink Shared Channel (HS-DSCH). The High-Speed Shared Control Channel (HS-SCCH), used as the downlink (DL) signaling channel, carries key physical layer control information to support the demodulation of the data on the HSDSCH. SF=1 SF=2 SF=4 SF=8

Modulation QPSK QPSK QPSK 16 QAM 16 QAM

Effective code rate 1/4 2/4 3/4 2/4 3/4

Max. throughput Mbps 5 codes 10 codes 15 codes 0.6 1.2 1.8 1.2 2.4 3.6 1.8 3.6 5.4 2.4 4.8 7.2 3.6 7.2 10.7

Table 1: Modulation and max throughput when 5,10,15 codes are allocated for a specific user

the necessary control data in the UL. User Equipment sends feedback information about the received signal2 quality on HS-DPCCH. That is, the UE calculates the DL Channel Quality Indicator (CQI) based on the received signal quality measured at the UE. Then, it sends the CQI on the HS-DPCCH channel to indicate which estimated transport block size, modulation type and number of parallel codes (i.e.; physical channels) could be received correctly with reasonable block error rate in the DL. The CQI is integer valued, with a range between 0 and 30. The higher the CQI is, the better the condition of the channel and the more information can be transmitted. To enable a large dynamic range of the HSDPA link adaptations and to maintain a good spectral efficiency, a user may simultaneously utilise up to 15 codes (physical channels) in parallel (Figure 2). The available code resources are primarily shared in the time domain but it is possible to share the code resources using code multiplexing. The relationship between modulation, the number of allocated codes and the maximum throughput is illustrated in Table 1. Fast scheduling and link adaptation are then performed promptly, depending on the active scheduling algorithm and the user-prioritisation scheme employed by the base station. In HSDPA, the AMC dynamically changes the Modulation and Coding Schemes (MCS) in subsequent frames in order to achieve high throughput on fading channels. HSDPA applies both QPSK (Quadrature Phase Shift Keying) and 16 QAM (16 Quadrature Amplitude Modulation) to transmit data over radio channels. The benefit of 16 QAM is that four bits of data are transmitted in each radio symbol as opposed to two in QPSK. 16 QAM increases data throughput, while QPSK is effective under adverse conditions. Depending on the condition of the radio channel, different levels of forward error correction (channel coding) can also be employed. For example, a three quarter coding rate means that three quarters of the bits transmitted are user-bits and the remaining one quarter are error- correcting bits. The process of selecting and quickly updating to the optimum modulation and coding rate is referred to as Fast Link Adaptation.

SF=16 Physical channels (codes) to which HS-DSCH is mapped SF HSDPA = 16 (example) Number of codes to which HSDPA transmission is mapped: 12 (example)

Figure 2: HSDPA mapping to physical channels (3GPP TR 25.848) The uplink (UL) signaling channel, called the High-Speed Dedicated Physical Control Channel (HS-DPCCH), conveys

3.

THE MODEL

We consider a wireless connection between a specified wireless user and its Node-B, and assume that an ideal feedback channel exists. A variant of the 2 In wireless communications, the quality of a received signal depends on a number of factors – the distance between the target and interfering base stations, the path-loss exponent, shadowing, channel-fading and noise.

P MM K k=1 CP Pk /GE/c/L G-queue [6] is introduced and employed in this paper for the steady state performance analysis of the downlink shared channel. The features and the assumptions of the present model are as follows: • The overall/effective arrival process is a P CP P process (at the transport block MM K k k=1 level). This process accounts for burstiness (through the batch arrivals of the CPP’s, which can indeed accommodate large batch sizes, and appropriate modulation of the arrival rate and batch size parameters), inter-arrival time autocorrelations (through the modulation). Thus, the superposition of several CPP arrival streams makes up this class of processes which is ideal for the present context. • Servers correspond to multicodes allocated for the specific UE under consideration in this study. The number of available servers is thus varying. • The whole system is modulated by a single Markov process which is the result of the combination (actually Kronecker sum) of three independent modulations: (i) the modulating process of the arrival traffic, (ii) the Markov process characterizing (modulating) the fading channel behavior [11], and (iii) the Markov process representing the channel allocation policy. • The process of packet loss in the air interface is modelled by the use of a negative customer CPP, in each modulating phase. This process can cater for the loss of single or multiple packets (customers) at a given time, in the air-interface. • L is the queuing capacity which can be finite or infinite. In this paper, we assume that no Automatic Repeat Request (ARQ) is performed at the physical layer. In the presence of ARQ, where a lost packet in the radio interface is retransmitted, the performance will be worse than the results obtained by the proposed model. Hence, in such a case, the numerical results generated by our model can be used as limiting results. In fact, we are able to model the loss in the physical interface. In a possible futuristic study, a new killing discipline, where an arriving negative customer removes a packet being served and adds a new packet P to the end of the queue, could be utilised in the MM K k=1 CP Pk /GE/c/L G-queue in order to accommodate the impact of ARQ in the link layer.

3.1

Packet arrival process

The arrival process is inherently modulated by a continuous time, irreducible Markov process, X, with NX states (i.e. phases of modulation). Let QX be the generator matrix of X. The arrival stream in each of the modulating phases of X comprise the superposition of K independent CPP [8] arrival streams of positive customers (referred to as customers or packets, hereinafter). Strictly, during the modulating phase i, the parameters of the GE inter-arrival time distribution of the kth (k = 1, 2, . . . , K) packet arrival stream are (σi,k , θi,k ). That is, the probability distribution function of inter-arrival times τi,k during phase i for the kth stream of customers is defined by Pr(τi,k = 0) = θi,k and Pr(0 < τi,k < t) = (1 − θi,k )(1 − e−σi,k t ). Packets are indistinguishable.

In phase i, in addition to the K streams of packets, there is also a CPP of negative customers. The use of this stream is to incorporate the loss of packets in the air interface.

3.2

Fading channel behavior

We assume that the degradations of a wireless channel in the air-interface can be described by the Nakagami-m fading channel. The received signal-to-noise ratio (SINR), γ, thereby has the Nakagami-m (or Rice) probability density function [11] given by,   mγ mm γ m−1 exp − , (1) fγ (γ) = m γ Γ(m) γ where γ = E(γ) is the average received SINR and Γ(m) = R ∞ m−1 t exp(−t)dt is the Gamma Function with parameter 0 m. Note that m is the Nakagami fading parameter (m ≥ 1/2). Since the CQI integer value sent by a UE varies between 0 and 30, we partition the range of the SINR into NZ = 31 intervals and use a continuous time first-order Markov chain (called Z) of NZ states to characterise the fading channel dynamics. That is, the SINR in state Si is associated with γ ∈ [γi , γi+1 ). Note that γ1 = 0, γNZ +1 = ∞. Each interval corresponds to a CQI value reported by a specific UE to its Node-B. The CQI corresponding to the fading channel state Si is i − 1, for i = 1, 2, . . . , NZ . These NZ intervals (partitions) are determined based on the equation between CQI and SINR as illustrated in [4]:  SINR ≤ -16  0 R (2) CQI = + 16.62c -16 < SINR < 14 . b SIN 1.02  30 SINR ≥ 14 The elements of the generator matrix, QZ , can be determined as follows QZ (k, k + 1) = ℵk+1 /πk (k = 1, 2, . . . , 30) QZ (k, k − 1) = ℵk /πk (k = 2, 3, . . . , 31)

(3)

The level crossing rate (ℵn ) of mode n (the AMC mode n is chosen when the channel is in state Sn ) is obtained as in [13]:  m−1   r mγn fd mγn mγn exp − , (4) ℵn = 2π γ Γ(m) γ γ (n = 1, 2, . . . , 31) and Z

γk+1

πk =

fγ (γ)dγ,

(5)

γk

where fd is the mobility-induced Doppler spread.

3.3

Physical channel allocation for a single user

The number of available physical channels (servers, in the model) for a specified user is determined by the channel assignment scheme (i.e. the resource allocation policy), which takes into account traffic to and from other users. There are a number of packet scheduling algorithms for the Node-B, which allocate resources according to different schemes or criteria, such as equal data amount for all users (up to a maximum allowed allocation), same resources (power/codes/time) for all users, same resources

(power/codes/time) per allocation time, etc [7]. This dynamic allocation results in a varying number of available (allocated) channels, with respect to a given user. In this paper, we construct a model which assumes that the available channels for the specified user is modulated by a Markov process, called U , with NU states and QU generator matrix.

3.4

Packet-loss process in the air interface

Zorzi et al [15] have shown that a Markovian approximation for the block error process can be a very good model for a broad range of parameters. Therefore, it is reasonable to model the packet loss process, in phase i, by an appropriate stream of negative customers. The inter-arrival time probability distribution of such a Markov renewal process for negative customers in phase i can be negative exponential, phase-type or GE. Which one is most appropriate is a question best decided by long-term research on practical systems. In our work, we choose the GE distribution with parameters (ρi , δi ). That is, the probability distribution function of inter-occurrence times (τi ) of packet losses, strictly during phase i is governed by Pr(τi = 0) = δi and Pr(0 < τi < t) = (1 − δi )(1 − e−ρi t ). We choose the GE distribution for a number of reasons. Firstly, GE negative customers allow the removal or killing of packets more than one at a time, which is the case in the air interface. Another reason is that the parameters of the GE distribution are determined by just the first two moments (where a match is possible) of sampled data. The GE distribution is the only distribution that is of least bias [8], if only the mean and variance are reliably computed from the samples. Moreover, for δi = 0, the GE distribution becomes exponential.

3.5

The queuing model

As discussed above, the arrival process, the wireless channel-fading and the channel allocation are modulated by the independent Markov chains X with NX states, Z with NZ states and U with NU states, respectively. If Y denotes the effective Markov chain jointly modulating the arrival process, the wireless channel-fading and the number of channels allocated, then Y can be determined quite easily from X, Z and U , with NY = NX × NZ × NU states or phases. The generator matrix of Y can be determined as the Kronecker sum of the generator matrices of X, Z and U. M M QY = QX QZ QU . (6) The queuing model (arrivals, services and number of available servers) is thus assumed to be inherently modulated by the Markov process Y . The parameters of the packet arrival process, the service process and c are determined from the functional parameters of the system. The operation of the queue, scheduling of customers, semantics of the negative customers in terms of the RCEkilling discipline with immune servicing and other necessary details are the same as explained in detail in [5, 6]. The state of the queue at any time t can be specified completely by two integer-valued random variables, I(t) and J(t). I(t) varies from 1 to NY , representing the phase of the modulating Markov chain Y , and 0 ≤ J(t) < L + 1 represents the number of positive customers in the system at time t, including any in service. The queue is now represented by a continuous time, discrete state Markov

process, V (V if L is infinite), on a rectangular lattice strip. Let I(t), the phase, vary in the horizontal direction and J(t), the queue length or level, in the vertical direction. We denote the steady state probabilities by {pi,j }, where pi,j = limt→∞ P rob(I(t) = i, J(t) = j), and let vj = (p1,j , . . . , pN,j ). The system evolves due to the following possible instantaneous transition rates: (a) qi,k – purely lateral transition rate – from state (i, j) to state (k, j), for all j ≥ 0 and 1 ≤ i, k ≤ NY (i 6= k), caused by a phase transition in the Markov chain Y modulating the entire system (qi,i = 0); (b) Bi,j,j+s – s-step upward transition rate – from state (i, j) to state (i, j + s), for all phases i, caused by a new batch arrival of size s positive customers. For a given j, s can be seen as bounded when L is finite and unbounded when L is infinite; (c) Ci,j,j−s – s-step downward transition rate – from state (i, j) to state (i, j − s), (j − s ≥ ci + 1) for all phases i, caused by either a batch service completion of size s or a batch arrival of negative customers of size s; (d) Ci,ci +s,ci – s-step downward transition rate – from state (i, ci + s) to state (i, ci ), for all phases i, caused by a batch arrival of negative customers of size ≥ s or a batch service completion of size s (1 ≤ s ≤ L − ci ); (e) Ci,ci −1+s,ci −1 – s-step downward transition rate, from state (i, ci − 1 + s) to state (i, ci − 1), for all phases i, caused by a batch departure of size s (1 ≤ s ≤ L − ci + 1); (f) Ci,j+1,j – 1-step downward transition rate, from state (i, j + 1) to state (i, j), (ci ≥ 2 ; 0 ≤ j ≤ ci − 2), for all phases i, caused by a single departure. ci is the number of servers allocated/available for the specified UE when I(t) = i. Obviously, cm is the largest among all ci ’s. The P system is therefore modelled as an K MM with varying c. k=1 CP Pk /GE/c/L G-queue, The Markov process representing the queue is of the QBD-U (Quasi multiple- simultaneous-unbounded births and deaths) type. The steady state probabilities and performance measures can be calculated following the methodology of [5, 6, 12], that is what we have used in our computations.

4.

NUMERICAL STUDY

In this section, we present a case study (i) to evaluate the performance of HSDPA with respect to a specified user (ii) to compare the performance of several UE category groups. Twelve UE categories have been defined by 3GPP. These categories are distinguished according to a number of factors that include the maximum number of HS-DSCH simultaneously received multicodes (5, 10 or 15), the minimum interTTI (Transmission Time Interval) time between the beginning of two consecutive transmissions to a specific UE, the maximum number of HS-DSCH transport block bits received within an HS-DSCH TTI, and the modulations (QPSK only or both QPSK and 16QAM) used.

0.1

1.2 1.18

Packet loss probability

Achieved throughput

1.16 1.14 1.12 1.1 1.08 1.06

UE cat. 3, 4 UE cat. 5, 6 UE cat. 7, 8 UE cat. 9 UE cat. 10

1.04

4

5

6

7 SINR

8

9

10

1.18

Achieved throughput

1.16 1.14 1.12 1.1 1.08 UE cat. 3, 4 UE cat. 5, 6 UE cat. 7, 8 UE cat. 9 UE cat. 10 5

6

7 SINR

8

9

10

Packet loss probability

0.1

0.01

UE cat. 3, 4 UE cat. 5, 6 UE cat. 7, 8 UE cat. 9 UE cat. 10

3

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7 SINR

8

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11

0.6 0.5 0.4 0.3

UE cat. 3, 4 UE cat. 5, 6 UE cat. 7, 8 UE cat. 9 UE cat. 10

0.2 0.1

4

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7 SINR

8

9

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Ratio between achieved and maximum throughput vs. SINR – GE traffic

0.9 0.8 0.7 0.6 0.5 0.4 0.3

UE cat. 3, 4 UE cat. 5, 6 UE cat. 7, 8 UE cat. 9 UE cat. 10

0.2 0.1

11

Figure 8: Figure 5: Packet loss probability vs. SINR – GE traffic

9

0.7

3

0.0001

8

Figure 7:

Ratio between achieved and maximum available throughput

Poisson traffic

7 SINR

0.8

11

Figure 4: Achieved throughput (in Mbps) vs. SINR –

0.001

6

0.9

3 4

5

traffic

1.02 3

4

Figure 6: Packet loss probability vs. SINR – Poisson

Ratio between achieved and maximum available throughput

1.2

1.04

UE cat. 3, 4 UE cat. 5, 6 UE cat. 7, 8 UE cat. 9 UE cat. 10

3

11

Figure 3: Achieved throughput (in Mbps) vs. SINR – GE traffic

1.06

0.001

0.0001

1.02 3

0.01

4

5

6

7 SINR

8

9

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11

Ratio between achieved and maximum throughput vs. SINR – Poisson traffic

0.1

We focus on the UE categories 5, 6, 7, 8, 9 and 10, which have inter-TTI= 1 and UE categories (3, 4), which have inter-TTI= 2. Based on the CQI mapping table for UE categories specified in [2], UE categories 3 and 4, UE categories 5 and 6, UE categories 7 and 8 have the same characteristics. Therefore 5 groups of UE categories are considered. We investigate a scenario where data is transferred from a network to a specified UE (with NU = 1), which means the number of allocated channels to a UE depends only on the channel state (i.e. the state of process Z). The queuing capacity at the Node-B of this specified UE is assumed to be 150. Traffic is assumed to follow the GE distribution3 with parameter pair (σ, θ), which are estimated from the Bellcore traffic trace BC-pAug89 available from the Internet Traffic Archive [1], based on the method of moment matching – see Table 4. That is, we assume NX = 1.

Table 2: Computed parameters of the GE interarrival time distribution We calculate the matrix QZ of size 31x31 following the method of Section 3.2 (note that QZ depends on m and the average SINR). The GE service parameters are determined from the monitored packet lengths in the trace and the transport block sizes of each UE at a specific CQI value [2]. The wireless channel behavior is modeled as the Nakagami-m channel, with m = 1. Note that this choice leads to the Rayleigh distribution [11], which is often used to model multipath fading with no direct line-of-sight (LOS) path. We also assume that the UE travels with a speed of 3 kmph. Therefore, the maximum Doppler frequency of the UE is fd = 5.6 Hz at 2 GHz carrier frequency. 0.1

0.08

PDF

0.06

0.04

0.02

0 5

10

15 CQI

20

0.08 0.07

PDF

0.06 0.05 0.04 0.03 0.02 0.01 0 0

5

10

15 CQI

20

25

30

Figure 10: PDF of CQI at the average SINR=10 dB

Arrival process σ (1/sec) θ 150.669890 0.526471

0

0.09

25

expected, UE categories 9 and 10 outperform other UE category groups in terms of achieved throughput and packet loss probability. The group of UE categories 3 and 4 suffers quite a large packet loss probability which does reduce to an acceptable value when the average SINR is high. However, when we plot the ratio4 between the achieved average throughput and the maximum available average throughput (the latter is calculated assuming there are always packets to be transmitted at Node B) in Figure 7, a different phenomenon is observed. This is that UE categories 9 and 10 did not fully exploit the capability of the HSDPA channel – from the network operation perspective; this shortcoming can be overcome if the channel is not reserved to the UE when there is no packet waiting in Node B. In addition, when SINR equals 4 dB, practically there is always a packet waiting at Node-B, and the channel efficiency factor is about 40%. The curves showing the performance of UE categories 5, 6, 7, 8, 9 and 10 in Figure 3 are quite suprising if one draws the probability density function (PDF) of CQI at the average SINR of 4 dB and 10 dB. It can be seen from Figures 9 and 10 that when the average SINR changes to 10 dB, the large CQI values have a higher probability. That is, more codes and a better modulation scheme can be allocated to a UE when the signaled CQI value is high. However, the improvement is very small, which is mainly due to the stochastic nature of the arrival process (packet arrivals at ‘wrong’ moments). To quantitatively show the difference between the presence of bursty traffic (GE) and Poisson traffic, we plot curves in Figures 4, 6 and 8 with similar parameters as in the previous figures, with the only exception that Poisson traffic of the same traffic intensity is assumed.

30

Figure 9: PDF of CQI at the average SINR=4 dB In Figures 3 and 5, the performance of UE Category groups versus the average SINR (in dB) is depicted. As 3 The choice of GE distribution for the delivery time is motivated by the fact that the GE distribution is a robust twomoment approximation of least bias, for any service time distribution [8].

5.

CONCLUSIONS

A new queuing model has been presented for the performance of HSDPA wireless channels with respect to a specified user. The model is essentially an interesting variant of the Sigma queuing model, but with a varying number of servers (channel allocations, c). It is denoted by the P MM K k=1 CP Pk /GE/c/L G-queue, with varying c (cm being the maximum of c). With certain reasonable assump4

maybe defined as a channel efficiency factor

tions, this integrated model is able to incorporate most of the salient features of HSDPA, such as traffic- burstiness, channel fading and channel-allocation policy, and to produce numerical results reflecting user-perspectives. This is the first time, to the authors’ best knowledge, that such a model has been conceived. We have presented numerical results (i) to evaluate the performance of HSDPA with respect to a specified user, (ii) to compare quantitatively different UE categories. We showed that UEs of higher categories cannot fully exploit the capability of the HSDPA, as expected. A number of new directions for further research do arise. One of these concerns the modeling of ARQ by a new negative customer killing discipline.

6.

REFERENCES

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[12] D. Thornley, H. Zatschler, and P. G. Harrison. An automated formulation of queues with multiple geometric batch processes. In HETNETS’03, July 2003. [13] H. S. Wang and N. Moayeri. Finite-State Markov channel-a useful model for radio communication channels . IEEE Transactions on Vehicular Technology, pages 163–171, 1995. [14] L.-L. Yang and L. Hanzo. Improving the Throughput of DS-CDMA Systems Using Adaptive Rate Transmissions Based on Variable Spreading Factors. In Proceeding of VTC 2002, Vancouver, volume 1, pages 1816–1820, September 2002. [15] M. Zorzi, R. R. Rao, and L. B. Milstein. Error Statistics in Data Transmission over Fading Channels. IEEE Trans. Commun., 46(11):1468–1477, November 1998.