Exploring Service and Buffer Management Issues toProvide Integrated Voice and Data Services inSingle and Multi Channel Wireless NetworksEser Gemikonakli

School of Science andTechnology

Middlesex University, UKEmail:e.gemikonakli@mdx.ac.uk

Glenford MappSchool of Science and

TechnologyMiddlesex University, UKEmail: g.mapp@mdx.ac.uk

Orhan GemikonakliSchool of Science and

TechnologyMiddlesex University, UK

Email: o.gemikonakli@mdx.ac.uk

Enver EverSchool of Science and

TechnologyMiddlesex University, UKEmail: e.ever@mdx.ac.uk

Abstract—Service and Buffer Management techniques can beused to ensure Quality of Service (QoS) for different traffic flowsaccording to some specific policies. In this study, a single bufferqueuing system is considered to model single and multi channel,homogeneous wireless network systems such as wireless local areanetworks (WLANs) and cellular networks. These systems are nowbeing used to carry both voice and data traffic and hence it isimportant to optimise these systems in an attempt to reduce theblocking, and minimize the latency to acceptable ranges. Sincevoice packets are delay sensitive, they have the priority to receiveservice. Also they require smaller buffering capacities, since theresponse time to voice requests should be below specific values.In addition, in order to reduce retransmission on reliable dataconnections, data packets are not usurped by incoming voicepackets. In this paper, a mathematical analysis of this scenariois explored.

The proposed mathematical model is represented by twodimensions; one for incoming voice packets and one for datapackets. The models proposed show that it is possible to storeincoming voice packets in the queue in case the channel or chan-nels are busy. Both voice and data packets have finite buffering.Incoming voice packets are blocked when the voice buffer orthe common queue is full. Therefore there is an added blockingprobability of voice due to the presence of data packets in thesystem when the common queue is full. The analytical modelis validated using simulation. The system proposed attempts toprovide minimum delay for voice while reducing the disruptionto reliable data connections. Numerical results show that, it ispossible to attain these goals with reasonable buffer sizes. Thisstudy is useful for understanding the trade-offs and thresholdsof single and multi channel systems with voice and data traffic.

Index Terms—Service Priority, Buffer Management, TrafficModels, Quality of Service, Two dimensional Markov chains.

I. INTRODUCTION

In modern communications, different wireless technologies(WLAN and cellular networks) play a significant role inproviding high throughput wireless Internet access, due to thewidespread acceptance of wireless technologies in enterpriseenvironments. This is mainly because of better bandwidth,the popularity of cellular phones, and the growing range ofmultimedia applications such as Skype. Multimedia trafficis the transmission of data representing various media withdifferent QoS requirements over communication networks.

The correlation between traffic and capacity on differentnetworks is one of the most critical issues because of thelimited availability of radio spectrum. Therefore, it is veryimportant to examine the capacity of systems with acceptableblocking probabilities and response times for each type oftraffic. This can be used as a measure of system resource forcomprehensive analysis [1].

Since voice packets are delay-sensitive, they differ fun-damentally from data traffic. Therefore, the use of wirelesssystems to transport real-time packets is a challenging task toprovide QoS for voice traffic while maintaining high through-put for data traffic [2], [3]. In cellular networks, traditionalsupport for multi-service traffic would involve the use ofchannel reservation schemes for voice packets. Such a policyis not applicable in single channel systems such as WLANs.However, it is possible to give service priority to voice traffic.In addition, due to higher data rates of WLAN, it has beenshown that a small amount of buffering can be used for voicepackets [4], [5]. However, while it is important to minimizedelay for voice packets, it is also essential to maintain reliabledata connections using transport protocols such as TCP/IP. Itis necessary to avoid dropping TCP packets as they wouldhave to be retransmitted. This action of course may lead toincrease blocking probability for voice packets. Hence, weavoid removing data packets, i.e., if incoming packets arriveand the buffer is full, data packets are not removed and so weincrease the blocking probability of voice due the presence ofdata packets, depending on the buffer size. This paper developsmathematical models to study this scenario for single and multichannel systems. This work challenges the assumption thatchannel reservation is the only way to provide acceptable QoSfor heterogeneous networks [6].

In this paper, a detailed traffic analysis is provided forsystems with various characteristics in terms of the number ofavailable channels and buffer capacities. A modified spectralexpansion solution approach [7] is employed for numericalresults. In Section II, the related work is considered. Theanalytical models are presented in Section III, and simulationprogram employed is explained in Section IV together with

validations of analytical models. Detailed analysis of inte-grated traffic is provided with numerical results for systemswith various characteristics in Section V. A summary isprovided with relevant conclusions in Section VI.

II. PREVIOUS WORK

Voice telephony is no longer the only available service inwireless and cellular systems. Multiple traffic systems nowconsist of integrated services with distinctive QoS require-ments. A number of different schemes have been proposedto deal with this problem. Though most of these schemesexplored mobility and multimedia characteristics, few studieshave considered the impact of buffering of voice packets inintegrated voice and data services. Therefore, we aim to makea critical investigation of existing traffic models and offergeneric models and traffic schemes for WLANs and cellularnetworks in order to analyse the impacts of buffering of voicepackets.

Traffic Management (TM) is known as the set of policiesand mechanisms to handle network congestion and poorperformance of a network. Call Admission Control (CAC),scheduling, and buffer management mechanisms can be com-bined in order to ensure high QoS for different serviceclasses [8]. Buffer management schemes can be categorisedinto three different classes: Complete Partition (CP) policybased, Complete Sharing (CS) policy based, and Partial BufferSharing (PBS) policy based [9]. PBS scheme is used to controldifferent priority classes based on thresholds in buffers [9],[10].

In [2], the authors investigated appropriate network buffersizing for voice traffic for 802.11 WLANs. Most of the recentworks focused on MAC design and operation; this study wasthe first to address the question of network buffer sizing forvoice traffic. The authors showed that the choice of buffersize has a significant impact on the average rate of successfulmessage delivery over a communication channel achieved byan Access Point (AP) and hence the need for a dynamicbuffering strategy [3]. Similarly in [5], the effects of usingpriority strategy, buffering, threshold control on the buffer,and channel reservation on the channel allocation schemeswere investigated for GPRS systems. Results in [5] showedthat it is possible to set a small amount of buffer for delay-sensitive voice packets and a larger buffer for non-delaysensitive data packets. Furthermore, channel reservation maydirectly improve the performance of a particular service whiledecreasing the performance of the other services significantly.

In [11], a congestion control system is developed to pro-vide high utilization and fairness for multi-server computersystems. Partial buffer sharing scheme with thresholds andblocking is used for two distinct priority traffic types. Asthe author mentioned in this paper, performance measuressignificantly change because of the impact of blocking factorand threshold policy. Therefore, a set of initial parameters forsuch systems should be chosen. These parameters are mainly;buffer capacity, the initial value for threshold, and blockingratio for both traffic types and also modification step level. As

previously mentioned, the results obtained from the proposedmodel can be used as the basis for the development of dynamicalgorithms in similar studies such as [11].

In [4], a generic traffic model is developed for a singlechannel WLAN network and the impact of buffering of voicepackets over data packets in integrated services is analysed.Prioritization of voice packets over data packets for the pro-posed model is the main policy, where data packets receiveservice if and only if there are no voice packets in the systemsince a single channel is assigned for both of the services.The results showed that a small amount of buffering for voicepacket, Lvc < 8, and larger amount for data packets shouldbe reserved.

The traffic model considered in this study is more genericthan the one considered in [5]. Furthermore, our proposedmodels are different from the model in [12] since we dealwith different traffic characteristics. Instead of reducing theinput rate of any service type, we do sensitivity analysis tofind trade-off between various parameters for integrated voiceand data services. The models presented are validated bysimulation, which considers the actual scenario in an eventtriggered fashion and not the Markov model. The models caneasily be adopted for different scenarios.

III. MODEL DESCRIPTION

A. SINGLE CHANNEL MODEL

An analytical, generic traffic model, is provided for perfor-mance evaluation of integrated voice and data packets within asingle channel homogeneous wireless communication system.The channel is assigned to two different types of traffic; real-time (voice) and non-real-time (data) traffic flows. In thissystem, voice is given service priority but both voice anddata packets are buffered in an integrated system. Therefore,Queuing theory and Markov chain analysis can effectivelybe used to investigate the operational spaces and limitationscaused by different characteristics of systems in terms of theblocking probability.

Fig. 1. The model of the system with finite buffering.

Fig. 1 represents the proposed model for two different typesof traffic (voice and data) based on the pre-emption policy. Theproposed scheme can be modelled as shown in Fig.2 using atwo-dimensional Quasi birth-death process. Pi,j is the steady-state probability for a state with i active voice packets and jactive data packets. Since the downward transitions are onlypossible for the states where there are no voice packets in thesystem (left most column of the Markov chain in Fig. 2), it ispossible to obtain all state probabilities in terms of P0,0, and aproduct form solution can be provided to solve such a systemas provided in [4].

The arrivals of voice and data packets are assumed to beindependent and follow Poisson distribution with mean arrivalrates σv and σd respectively. The service times of voice anddata packets, are assumed to follow exponential distributionwith means 1/µv for voice packets and 1/µd for data packets.

The maximum number of voice packets allowed in thesystem is equal to one voice packet assigned to the channel(S = 1) in the system plus the queuing capacity Bvc (in Fig.1). The maximum number of voice packets in the system isgiven by Lvc, where Lvc = S + Bvc. On the other hand, thenumber of data packets accepted in the system is equal to onedata packet being serviced plus queuing capacity Bdt (in Fig.1). The maximum number of data packets in the system isgiven by Ldt, where Ldt = S +Bdt and Bdt > Bvc.

Fig. 2. The state transition diagram for the performance model of the systemconsidered with finite queuing capacity.

1) Service Prioritization of Voice packets: For the pre-emptive method, an ongoing data packet is buffered and itschannel is allocated to an incoming voice packet. Since asingle channel is assigned to both voice and data, where thevoice has service priority the data packets do not receiveservice if the voice queue is not empty.

2) Buffer Management for Integrated Voice and Data Ser-vices: The flowchart showing buffer management is given inFig. 3 to show the admission of voice and data packets to thesystem. When there is a new packet; for voice packets, if thechannel is available then the request is assigned to the channel.If the channel is not available, then if voice is currently beingserved, the incoming voice packet is queued if the buffer isnot full or else the incoming packet is blocked. However, ifdata is being served, it is pre-empted by the incoming voicepacket and if there is a room in the buffer the pre-empted datais queued or else it is blocked. For data packet arrivals, first,the number of voice packets that are in the system is checked.If there are voice packets in the system then the incoming datapacket is queued if the queue is not full. If the queue is full,it is blocked. If there are no voice packets in the system andthe channel is busy (then another data packet is being served)

the data packet has to be queued if the buffer has free spaceor blocked if it is full. If the channel is not busy data packetreceives service.

Fig. 3. Flowchart of the traffic flows with finite buffering.

B. MULTI CHANNEL MODEL

The multi channel model presented is similar to singlechannel Markov chain. Any one of the channels can beassigned to real-time (voice) and non-real-time (data) trafficflows. The priority is again given to the voice packets in thesystem.

The data packets do not receive service if the number ofvoice packets in the queue is higher than or equal to thenumber of channels in the system. When there is a new voicepacket, if there is an available channel, then the request isassigned to the channel. If all the channels are busy withvoice packet requests, the incoming voice packet is queuedif the buffer is not full or else the incoming packet is blocked.However, if there are channels busy with data requests, one ofthe data requests is pre-empted by the incoming voice packet.If there is a room in the buffer, the pre-empted data is queuedotherwise it is blocked.

For data packet arrivals, first, the channels are checked andif they are all busy either with voice or data packet requests,then the incoming data packet is queued if the queue is not full.If the queue is full, it is blocked. If the channel is not busy datapacket receives service. The Markov chain for representing thestates of the multi-channel system is provided in Fig. 4.

Voice and data packets are buffered in an integrated sys-tem. Therefore, queuing theory and Markov chain analysiscan effectively be used to investigate the operational spacesand limitations caused by different characteristics of systems.However it is not possible to use the method in [4] to have aproduct form solution for the multi channel case. It is possibleto solve the system for state probabilities, as a system ofsimultaneous equations for an exact solution, however thiswould be quite costly in terms of the computation time. In thisstudy an approximated version of spectral expansion solutionapproach has been adopted for more efficient calculations.

It is possible to extend the solution methodology presentedin [7] for performance evaluation, and buffer analysis of two

Fig. 4. The state transition diagram for the performance model of the system considered with finite queuing capacity and multi-channel.

stage open queuing models which is used to represent theintegrated voice and data traffic. Let the number of voicepackets in the system, (I(t)), be represented in the horizontaldirection and possible number of data packets (J(t)), berepresented in the vertical direction of a lattice strip. MatricesA, B, and C [7] are used to represent purely lateral, onestep upward and one step downward transitions similar to[7], and the resulting system is solved for the steady stateprobabilities using the steady state solution presented in [7].In the spectral expansion solution approach used, there aretransitions to the states where the total number of voice anddata packets can be higher than Ldt. In other words whenFig. 4 is considered, the states at the top right corner of thelattice can be visited, however they have significantly lowerstate probabilities. For systems where the states on top rightcorner are visited with high probabilities, spectral expansiondoes not give good approximations and system of simultaneous

equations is employed. A custom simulation package hasbeen developed to simulate the scenario explained above forvalidation of the approximation used. The details are providedin section IV. The details of the spectral expansion methodemployed can be found in [7].

IV. SIMULATION

Our objective in this section is to provide an overview ofthe developed simulation tool. The simulation tool is mainlyused for validation of the models developed, however it can beused for performance evaluation of various scenarios since itsimulates the actual scenario rather than the Markov models.

A discrete event simulation (DES) approach is implementedfor the queueing processes since it is more effective andcomputationally less expensive for queueing theory. Therefore,our discussion in this section is restricted to discrete-eventsimulation (DES). A DES model is defined as one in whichthe state variables change only at those discrete points in

time at which events occur [13]. Well known queueing theoryformulae for systems such as M/M/1/L and M/M/S/L areused for validating the simulation in development phase.

The simulation developed considers the stochastic pro-cesses; both type of packet arrivals and departures occur oneat a time in a random discrete event triggered fashion when apacket enters the system and service is completed respectively.Once the voice and data packets join to the queue, theyultimately receive service at some time. However, data packetsare only served when there are no voice packets in the queueeven when the multi-channel system is considered. This isdue to the priority given to voice packets over data packets.The packets waiting in the queue are served in order of theirarrival, first in first out (FIFO), by single or multi channelsystems. When the service event is completed, the channel(channels) becomes idle or remains busy with requests whichwere stored in the queue. While a particular event is handled,the next event is generated.

Please note that the traffic intensity for data and voice pack-ets are defined as ρd and ρv respectively where ρd = λd/µd

and ρv = λv/µv . Similarly the traffic intensity per server isdefined as ud = ρd/S and uv = ρv/S for data and voicepackets respectively.

In order to validate the proposed analytical model, theresults obtained from the analytical model are presentedcomparatively with the simulation results for different voicetraffic load per server (uv) in Table I and II. For both typesof packets, Mean Queue Lengths (MQLv and MQLd forvoice and data respectively) are considered in Table I. Thetable shows the discrepancy for MQLv and MQLd resultsrespectively, where S = 8, ud = 0.5 packet/ms, Lvc = 16and Ldt = 100. The maximum discrepancies between theanalytical solution and simulation are less than 0.3475% and1.6994% for MQLv and MQLd respectively. In Table II,Blocking Probability and Response Time of voice packets(Bpv and Rtv) are considered. The maximum discrepanciesbetween the analytical solution and simulation are less than0.9270% and 0.3566% for Bpv and Rtv respectively.

TABLE ICOMPARATIVE RESULT 1

Mathematical model Simulation Discrepancy(%)

uv Mqlv Mqld Mqlv Mqld Mqlv Mqld0.1 0.80 4.2036 0.7989 4.2025 0.1381 0.02480.3 2.4015 5.6858 2.4033 5.7824 0.0751 1.69940.35 2.8047 6.9469 2.8057 6.9440 0.0346 0.04210.6 4.4291 86.6143 4.4318 86.3202 0.0593 0.33950.9 5.2133 92.4462 5.2290 92.1479 0.2992 0.32270.92 5.2535 92.5131 5.2710 92.1975 0.3312 0.34110.95 5.3118 92.5979 5.3085 92.3633 0.0631 0.25340.98 5.36769 92.6676 5.3864 92.3644 0.3475 0.32720.99 5.3858 92.6880 5.3873 92.4105 0.0270 0.2994

In order to further emphasise the accuracy of the analyticalmodel, Fig. 5 and Fig. 6 are presented. MQLv and MQLd

results are given as functions of uv . The simulation software isdeveloped in C++ language and validated to simulate the actual

TABLE IICOMPARATIVE RESULT 2

Mathematical model Simulation Discrepancy(%)

uv Bpv Rtv Bpv Rtv Bpv Rtv

0.1 0 12.50 0 12.4614 0 0.30880.3 0 12.5078 0 12.5525 0 0.35660.35 0 12.5210 0 12.5129 0 0.06490.6 0.0909 12.6884 0.0903 12.6553 0.7084 0.26150.9 0.2857 12.67162 2.84E-01 12.6876 0.6086 0.12600.92 0.2957 12.6702 2.93E-01 12.6717 0.9270 0.01160.95 0.3103 12.6682 0.3114 12.6840 0.3555 0.12470.98 0.3243 12.66628 0.3243 12.6866 0.0090 0.16030.99 0.3288 12.6656 0.3281 12.6598 0.2228 0.0463

system. Each result obtained from the simulations is within theconfidence interval of 5% with a confidence level of 95%. Alaptop with 2.40 GHz Intel(R) Core(TM)2 Duo processor, 4GB RAM and MS V C + + 10.0 is used to achieve all theresults presented in this study.

0

2

4

6

8

10

12

uv

MeanQueu

eLen

gth(M

QLv)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

20

40

60

80

100

120

140

MeanQueu

eLen

gth(M

QLd)ud = 0.5, µv = 0.08, µd = 0.06

AnalyticalMethod, MqlvSimulation, Mqlv

AnalyticalMethod, MqldSimulation, Mqld

S=4, Lvc

=8, Ldt

=50

S=8, Lvc

=16, Ldt

=100

S=16, Lvc

=32, Ldt

=150

S=16, Lvc

= 32, Ldt

=150

S=8, Lvc

=16, Ldt

=100

S=4, Lvc

=8, Ldt

=50

Fig. 5. Mean Queue Length for voice and data packets as uv increases.

10−15

10−10

10−5

100

uv

BlockingProbability(B

pv)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 112.4

12.6

12.8

13

13.2

13.4

13.6

13.8

Response

Tim

e(R

tv)

ud = 0.5, µv = 0.08, µd = 0.06

AnalyticalMethod, Bpv

Simulation, Bpv

AnalyticalMethod, Rtv

Simulation, Rtv

S=4, Lvc

=8, Ldt

=50

S=8, Lvc

=16, Ldt

=100

S=16, Lvc

=32, Ldt

=150

S=4, Lvc

=8, Ldt

=50

S=8, Lvc

=16, Ldt

=100 S=16, Lvc

=32, Ldt

=150

Fig. 6. Blocking probability and Response time for voice packets as uvincreases.

V. NUMERICAL RESULTS AND DISCUSSIONS

Numerical results are presented in this section in order toshow that it is possible to buffer voice packets, while theresponse time is still acceptable, i.e., less than 100 ms [4]and data packets receive desired levels of QoS.

The parameters used in the mathematical calculations areas follows: Mean service rate for voice packets (µv) and

mean service rate for date packets (µd) are 0.08 and 0.06 msrespectively. The other parameters used are varying dependingon the limitation of the system.(i.e number of channels, meanarrival rates and utilization of channels).

Please note that the voice packets are blocked if the numberof voice packets are larger than Lvc or the total number ofvoice and data packets are equal to the maximum buffer size,Ldt. Therefore, blocking probability for voice calls in theproposed models can be calculated as given in eqn. (1).

Bpv =

Ldt−Lvc∑j=0

PLvc,j +

Lvc−1∑i=0

Pi,Ldt−i (1)

The first term of the equation is the blocking probability ofvoice due to the finite storage capacity of Lvc. On the otherhand the second term is the blocking probability due to thepresence of data. In this paper, we define blocking probabilitydue to the presence of data as δx.

δx =

Lvc−1∑i=0

Pi,Ldt−i (2)

Fig. 7 shows the blocking probabilities of voice packets asa function of data traffic load per server (ud) for different Ldt

values. The results show that as ud increases, the blockingprobability for voice packets increases as well. It is alsoshown that the voice blocking probability decreases as databuffer capacity increases. The system reaches saturation atud = 0.6125. At this point, the buffer capacity makes littledifference for Ldt = 400 and Ldt = 600. This means thatwhen uv + ud ≥ 1 the system reaches saturation regardlessof the buffer capacity, and the buffer capacity of the wirelesssystem does not affect the system performance. This verifiesthat the integrated systems obey the known limitation ofgeneral queuing network systems.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 15

6

7

8

9

10x 10

−3

ud

Blockingprobability(B

pv)

S = 1, Lvc = 5, uv = 0.3875

Ldt = 30Ldt = 100Ldt = 400Ldt = 600Ldt → ∞

Fig. 7. Blocking Probability of voice packets as ud increases.

Fig. 8 shows the effects of ud on the cost of data packetsover voice packets, i.e. δx for different Ldt values. The resultsin Fig. 8 clearly show that, when the overall buffer size islarge (e.g Ldt = 400), the cost of data packets δx is verysmall (almost zero). Therefore the effects of data on voicepackets can be minimized by using large buffers and can alsobe controlled by varying the buffer size. However, the figurealso shows that this is only true when uv + ud < 1.

Fig.9 shows the effects of ud for different channel andbuffering capacities for voice packets and Ldt = 100. Theδx is given as a function of ud for different uv and Ldt valuesand constant Lvc in Fig. 10. Results in Fig. 9 and Fig. 10 showthat, the effect of data packets on voice packets can be dealtwith by varying the buffer size and/or increasing the numberof channels for the integrated services, as long as uv+ud < 1.

It is possible to employ the models presented and thesimulation to further explore the buffering characteristics. It ispossible to specify the sizes of the buffer which can minimisethe δx, in other words the sizes of buffer where the voicepackets behave independent of the data, like an M/M/S/Lvc

system.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

ud

δx

S = 1, Lvc = 5, uv = 0.3875

Ldt = 30Ldt = 400

Fig. 8. The cost of data packets over voice packets as ud increases.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

ud

δx

uv = 0.6, Ldt = 100

Lvc = 16, S = 5Lvc = 16, S = 8Lvc = 30, S = 5Lvc = 30, S = 8

Fig. 9. δx for various Lvc and S as ud increases.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

ud

δx

S = 8, Lvc = 16

Ldt = 50, uv = 0.6

Ldt = 400, uv = 0.6

Ldt = 50, uv = 0.9

Ldt = 400, uv = 0.9

Fig. 10. δx for various Lvc and uv as ud increases.

The amount of buffering required to make the integratedsystems perform like M/M/1/Lvc and M/M/S/Lvc is ex-

plored in Fig. 11 and Fig. 12 respectively. The Ldt valuerequired for the systems to perform like M/M/1/Lvc andM/M/S/Lvc is considered as a function of ud. In other wordsthe buffer capacities (Ldt) required to make sure data packetsdo not affect the voice packets are specified for different dataloads. The results are also presented for various values of uv .According to the the results in both figures, this is possiblefor the single channel system for Ldt ≥ 400, and for multichannel systems when Ldt ≥ 133.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8050

200

400500

1,000

1,500

2,000

ud

Totalsystem

capacity(L

dt)

S = 1, δx = 0, Lvc = 5

uv = 0.125uv = 0.3875uv = 0.625

Fig. 11. Analysis of Ldt for single channel systems.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

50

100

133150

200

250

300

ud

Total

System

Cap

acity(L

dt)

S = 8, Lvc = 16, δx = 0

uv = 0.1uv = 0.6uv = 0.9

Fig. 12. Analysis of Ldt for multi channel systems.

0 0.5 1 1.5 2 2.5 310

−20

10−15

10−10

10−5

100

σv

Blockingprobability(B

pv)

0 0.5 1 1.5 2 2.5 3

0

50

100

150

200

250

300

350

Response

time(R

td)

S = 32, Lvc = 50, Ldt = 100, µv = 0.08, µd = 0.06

ud = 0.1, Bpv

ud = 0.5, Bpv

ud = 0.9, Bpv

ud = 0.1, Rtd

ud = 0.5, Rtd

ud = 0.9, Rtd

Fig. 13. Blocking Probability for voice traffic and Response Time for datatraffic for multichannel systems.

Fig. 13 shows the Blocking Probability for voice packetsand Response Time for data packets as a function of σvfor different ud values. The results show that as the arrivalrate of the incoming voice packets increase, the Response

Time for the data packets increase. The increase is morerapid for the smaller ud values when the mean arrival ratefor σv > 1.5. When data load in the system is high, theresponse time reduces significantly compared to the smallerdata loads, and therefore, increasing σv does not affect thesystem significantly. This is because the data packets dominatethe system and therefore as Fig 13 shows, voice packets areblocked. Hence, Response Time for data packets are decreased.

Fig. 14 shows the MQL for voice packets as a function ofσv for various Lvc. The results show that as Lvc increases,the upper-bound for MQLv increases. However for relativelysmall loads of voice traffic, the Lvc does not affect the systemsignificantly.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

2

4

6

8

10

σv

MeanQueu

eLen

gth(M

QLv) S = 8, ud = 0.1, Ldt = 100

Lvc = 8Lvc = 10Lvc = 12Lvc = 16

Fig. 14. Mean Queue Length for voice packets as a function of σv .

2.5

3

3.5

4

4.5

5

Lvc

MeanQueu

eLen

gth(M

QLv)

5 6 7 8 9 10 11 12 13 14 150

20

40

60

80

100

120

140

MeanQueu

eLen

gth(M

QLd)uv = 0.6, ud = 0.4, Ldt = 150, µv = 0.08, µd = 0.06

S = 5, MQLvS = 6, MQLvS = 7, MQLvS = 8, MQLv

S = 5, MQLd

S = 6, MQLd

S = 7, MQLd

S = 8, MQLd

Fig. 15. Mean Queue Length for voice and data packets as function of Łvc

for various S.

Fig. 15 shows the effects of Lvc on the MQL of voice anddata packets for uv = 0.6 and ud = 0.4 and different numbersof channels. The results show an increase in MQLv as Lvc

increases for Lvc < 15. However, if the response time is inacceptable levels [4], increasing the queuing capacity of thevoice packets further, does not affect the system. However,increasing the number of channels affect the MQLv . WhileMQL for voice packet is increased, MQL for data packets isdecreased.

VI. CONCLUSION

In this study analytical models are presented together withsimulation results for single and multi channel wireless com-munication systems with integrated voice and data packetrequests.

This work shows that, the buffering scheme proposed tostore packets from various traffic sources is as important asthe prioritization of traffic classes to understand overall systemperformance. Not removing data packets from a full buffer atthe arrival of a new voice packet results in increased blockingprobability for voice packets. However the analysis performedshows that with larger buffer capacities, it is possible to avoidthis since the results tend to be same as M/M/1/Lvc, andM/M/S/Lvc. These results are also significant as they showthat it is possible to support both voice and data using ascheme where voice is given service priority but there isa small amount of buffering for voice packets and a largeramount of buffering is reserved for data packets. The keyobservation is that since most data connections on the Internetuse TCP/IP which is reliable, dropping data packets will resultin retransmissions which tie up network resources. Hence it isalways better from network point of view to avoid droppingdata packets. The analysis shows that having Lvc < 8 andLdt > 400 for a single channel system, result in providinga stable and optimum environment for these traffic types.The results obtained for the multichannel systems, also showsthat having Lvc < 15 and Ldt > 133 , results in providingoptimum results (δx = 0) where the integrated system tend tobe same as M/M/S/Lvc where S ≥ 5.

Finally, this work is not only relevant to single channelWLAN systems, or multi channel cellular systems but is alsorelevant for wired systems such as ingress routers which mustserve multi-service traffic such as voice and data over severalinterfaces. Dynamic queue management techniques in routershave not previously considered traffic classes and are basedaround reduced threshold values [12], [14]. This paper showsthat future dynamic queue management algorithms should takeinto account traffic class characteristics in order to provideefficient routing algorithms in multi server environment. Forfurther work we would like to model video traffic as wellprobably using Batch process arrival. Once we have developeda generic model, we aim to design mobility-dependent QoSframework to support the high capacity demand which isrequired for voice, data and video traffic in networks.

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