PERFORMANCE ANALYSIS OF
SOME RESOURCE ALLOCATION METHODS IN WIRELESS CELLULAR NETWORKS
Ph.D. Dissertation Summary by
Nam Hoai Do
Department of Networked Systems and Services Faculty of Electrical Engineering and Informatics Budapest University of Technology and Economics
Research Supervisor:
Prof. Tien Van Do
Budapest University of Technology and Economics
Budapest, Hungary 2013
1 Motivations and purposes
Performance evaluation plays a key role in the efficient operation of ICT (Information and Communication Technologies) because the capacity and resource can be dimen- sioned by the application of advanced modelling techniques [17, 29]. More than ten years ago, an intensive research collaboration was started between R. Chakka and the research group of T.V. Do. The fruitful cooperation has achieved a number of results (see [5, 6, 7, 8, 15, 17] and references therein). The aim of my research has been formu- lated within the framework of the collaboration. The goals are to apply and enhance methods [5, 6, 7, 8, 15, 17] for
• analysing certain scenarios in the application of High Speed Downlink Packet Ac- cess (HSDPA) for Communications Networks based on High Altitude Platforms,
• modeling a radio spectrum renting in mobile cellular networks,
• establishing an efficient algorithm for the M/M/c retrial queue with impatient customers.
2 Research Methodology
This section provides the short overview of methodology applied to solve the problems in this dissertation. It is worth emphasizing that performance evaluation can be carried out by either using a simulation program, or using a mathematical analysis with explicit performance expressions or numerical procedures, or build the system and then measure its performance [22, 23]. Mathematical analysis often results in methods of lower computational effort than performance evaluation using stochastic simulation [13, 17, 29].
The Quasi Birth-Death (QBD) framework is a well known technique for the perfor- mance evaluation of many problems in telecommunications and computer networks [3, 4, 19, 24, 26, 27, 30]. The state space of a QBD process is described by two random variables: a phase and a level [24, 25, 27]. Transitions in a QBD process are possible only within the same level or between adjacent levels.
Two well known methods to solve steady state probabilities of a QBD process are Matrix-Geometric Method (MGM) [19, 27] and Spectral Expansion Method (SEM) [4, 25]. Other methods to compute the steady state probabilities of a QBD process can
be found in [21, 28]. The detailed comparison of methods for QBD processes can be found in [29].
In the MGM, a nonlinear matrix equation is first formed from the system param- eters. Then, the minimal nonnegative solution R of this equation is computed by an iterative method. The invariant vector is then expressed in terms of the powers of R.
However, the number of iterations which are needed to computeRto a given accuracy is unknown. It is shown that for certain parameter values the computational efforts are uncertain and formidably large. Some improved algorithms of the MGM were proposed to enhance the computation ofR [3, 24, 26].
The SEM is based on expressing the invariant vector of the process in terms of the eigenvalues and the left eigenvectors of the matrix polynomial to compute the steady state probabilities.
Recently, two new queuing models, the M M PK
k=1CP Pk/GE/c/L G-queue with homogenous servers –known as the Sigma queue [7], and with heterogeneous servers –theHetSigmaqueue [6] were proposed with application of the SEM. These models do provide a larger flexibility to accommodate geometric as well as non-geometric batch sizes in both arrivals and services, and hence are capable of emerging as generalized Markovian node modelsorgeneralized Markovian queues (GMQ), with proven suitabil- ity [6, 7, 9] for modeling many aspects of the emerging telecommunication systems and networks.
The SEM is also applied to solve retrial queues [12, 16] that can be used to take into account a phenomenon in modern information and telecommunication systems where blocked customers may re-request for service after a certain timeout [2, 20]. Do also proposed some enhanced numerical computation algorithms for computing steady state probabilities with application of the SEM [10, 11, 14].
The contributions of this thesis are derived based on the exploitation of the proper- ties of Quasi Birth-Death (QBD) processes, the SEM method, the MGM method, the Sigmaand HetSigma queues.
3 New Results
My achieved results can be categorized into three groups of claims.
Claim 1: Analysing certain scenarios in the application of HSDPA for Communications Networks based on High Altitude Plat- forms (HAPs) [J1, C1]:
A performance of User Equipments (UEs) in HAP based HSDPA networks is investi- gated using a variant of the Sigma queueing model [J1, J2] with varying number of servers in an integrated way [C1]. The analytical model is validated with the ns-2 based EURANE simulator using Auckland Internet traffic trace [1] and a channel behavior of HAP environments (Chapter 2 of the thesis).
My specific contributions are summarised as follows:
• Claim 1.1: I incorporated the HAP channel model (Subsection 2.4.2) into the queueing model, which is able to capture the features of wireless communications, such as traffic-burstiness, channel fading, channel allocation policy, etc., in an integrated way (Subsection 2.4.1).
• Claim 1.2: I developed a method to validate the proposed analytical model us- ing real traffic traces as Auckland Internet traffic trace, and a channel behavior (Subsection 2.4.3.1).
• Claim 1.3: I showed that the performance experienced by pedestrian users does vary a lot with angle of elevation of the HAP (Figure 2.7).
Claim 2: Modeling a radio spectrum renting in mobile cellular networks [J3]:
A new queueing model is proposed to investigate an application of a radio spectrum renting in mobile cellular networks, where network operators can utilize the radio spectrum renting to increase the efficiency of the spectrum usage and to relieve a temporary capacity shortage of a particular cell (see Chapter 3 of the thesis). Some aspects of the renting policy are integrated simultaneously involving a block of user channels and call admission control in wireless cellular networks in one analytical model.
The proposed queueing model is validated with a simulation, in which call durations follow the log-normal distribution.
My own contributions are summarised as follows:
• Claim 2.1: I proposed a spectrum renting policy (Subsection 3.3.2) based on a hysteresis control with two thresholds for the network operator to rent or give back frequency bands based on the offered traffic as illustrated in Figure 3.1.
• Claim 2.2: I provided an analytical model for modeling a mobile cellular network with the proposed radio spectrum renting policy (Section 3.3). The model takes into account that (i) a rented frequency band accommodates the number of user channels and (ii) several variants of the Fractional Guard Channel Policy. Then I constructed a two dimensional Continuous Time Markov Chain (CTMC) based on the proposed model (Section 3.4).
• Claim 2.3: I showed that the proposed queueing model can accurately evaluate mobile networks with call durations following the log-normal distribution (See Figures 3.2-3.4) and only the radio spectrum renting can be used to decrease the blocking probability of fresh calls without compromising the grade of service of handover calls (See Figures 3.2-3.7).
Claim 3: Establishing an efficient algorithm for the M/M/c retrial queue with impatient customers [J4]:
A new algorithm is proposed to enhance the HM2 algorithm of Domenech-Benlloch et al. [18], that enable the approximation of a performance of a multiserver retrial queue with impatient customers. Exact expressions are derived for the computation of the rate matrixRand the conditional mean number of customers (It is worth emphasizing that matrix R is computed with a method proposed in [14]). The behavior of perfor- mance measures versusN is explored, then an estimation of the thresholdN is derived.
Based on the derivations, an efficient algorithm is constructed for the stationary dis- tribution with the determination of the threshold N that allows the computation of performance measures with a specific accuracy (see Chapter 4 of the thesis).
My contributions are summarised as follows:
• Claim 3.1: I derived exact expressions for the computation of the conditional mean number of customers (Corollary 2) after obtaining the closed form of R using the method proposed in [14] (See Theorem 1). Corollary 2 expresses that the conditional mean value M(N) = E[J|J ≥ N] of the number J of customers in the orbit under the condition J ≥N is a simple function of a single eigenvalue and N.
• Claim 3.2: I explored the behavior of performance measures versusN (Subsection 4.3.3) and then derived an estimation of the threshold N (Subsection 4.3.4).
• Claim 3.3: I provided an efficient algorithm for the stationary distribution (See Algorithm 2 and Algorithm 4) with the determination of the threshold N (See Algorithm 3) that allows the computation of performance measures with a specific accuracy.
• Claim 3.4: I showed that the computational time complexity of our algorithm is of O(c) (See Figures 4.11-4.13) and has the same accuracy as of the original HM2 algorithm (Table 4.1).
4 Application of the results
The achieved results are useful tool to determine an appropriate resource for respective systems.
The results in first claim group show that the proposed analytical model is useful tool to model HSDPA networks and also confirm the applicability ofSigma and Het- Sigma queueing models for modeling many aspects of the emerging telecommunication systems and networks.
The proposed analytical model in Chapter 3 is applicable in performance evaluation of mobile cellular networks with application of a radio spectrum renting. It also can be used to compare an efficiency of radio spectrum renting policies.
The results in the third claim group show that the computational time complexity of our algorithm is ofO(c). Hence it is especially applicable to a computation of retrial queues with impatient customers, in which the numberc of servers is very large.
Own publications related to this thesis
[J1] Tien Van Do and Ram Chakka and Nam Hoai Do and L´aszl´o Pap. A Marko- vian Queue with Varying Number of Servers and Applications to the Performance Comparison of HSDPA User Equipment. Acta Informatica, 48(4):243–269, 2011.
(IF=0.444)
[J2] Tien Van Do andNam Hoai Doand Ram Chakka. A Performance Model for the HSDPA User Equipment and its Validation. Journal on Information Technolo- gies and Communications - Research Development and Application on Electronics Telecommunications and Information Technology, 4:3–10, 2008.
[J3] Tien Van Do and Nam Hoai Do and Ram Chakka. A New Queueing Model for Spectrum Renting in Mobile Cellular Networks. Computer Communications, 35(10):1165–1171, June 2012. (IF=1.044*)
[J4] Tien Van Do,Nam Hoai Do, and Jie Zhang. An Efficient Computational Method for Retrial Queues with Impatient Customers. Computers & Industrial Engineer- ing, DOI:10.1016/j.cie.2013.04.008, 2013. (IF=1.589**)
[C1] Tien Van Do and Nam Hoai Do and Ram Chakka. Performance Evaluation of the High Speed Downlink Packet Access in Communications Networks Based on High Altitude Platforms. Lecture Notes in Computer Science, 5055:310–322, 2008.
Other own publications
[J5] Gerg˝o Buchholcz and Do Hoai Nam and Luong Dinh Dung and Do Van Tien. Vezet´ekn´elk¨uli, adapt´ıv k´odol´asos ´es modul´aci´os h´al´ozatokban alkalmazhat´o
¨
utemez´esi algoritmus. Magyar T´avk¨ozl´es, XVII(2):8–12, 2006.
[J6] Nam Hoai Do and Dung Dinh Luong. A novel Packet Scheduling for Wireless Channels with Adaptive Burst Profile. Journal on Information Technologies and Communications - Research Development and Application on Electronics Telecom- munications and Information Technology, 4:18–24, 2008.
[C2] Dung Dinh Luong and Nam Hoai Do and Gerg˝o Buchholcz and Tien Van Do. Packet Fair Scheduling for Wireless Channels with Adaptive Burst Profiles.
In International Workshop on High Altitude Platform Systems (WHAPS 2005), pages 1–7, Athens, Greece, September 2005.
[C3] Dung Dinh Luong andNam Hoai Do. Cross-layer design of packet scheduling algorithm. In 13th International Conference on Software in Telecommunications and Computer Networks, (SoftCOM2006), pages 76–80, Split, Croatia, September 2006.
Bibliography
[1] Auckland Internet Traffic Capture (2001)
http://www.wand.net.nz/wits/auck/6/20010612-060000-e1.php.
[2] Artalejo, J. R. and G´omez-Corral, A. (2008) Retrial Queueing Systems. Springer- Verlag, Berlin Heidelberg.
[3] Bini, D. A., Latouche, G., and Meini, B. (2005) Numerical Methods for Struc- tured Markov Chains (Numerical Mathematics and Scientific Computation). Ox- ford University Press, Inc., New York, NY, USA.
[4] Chakka, R. (1995) Performance and Reliability Modelling of Computing Systems Using Spectral Expansion. PhD thesis University of Newcastle upon Tyne (New- castle upon Tyne).
[5] Chakka, R. and Do, T. V. (2002) The M MPK
k=1CP Pk/GE/c/L G-Queue and Its Application to the Analysis of the Load Balancing in MPLS Networks. 27th Annual IEEE Conference on Local Computer Networks (LCN 2002), 6-8 November 2002, Tampa, FL, USA, Proceedings, pp. 735–736.
[6] Chakka, R. and Do, T. V. (2007) The MM PK
k=1CP Pk/GE/c/L G-Queue with Heterogeneous Servers: Steady state solution and an application to performance evaluation. Performance Evaluation,64, 191–209.
[7] Chakka, R., Do, T. V., and Pandi, Z. (2009) A Generalized Markovian Queue and Its Applications to Performance Analysis in Telecommunications Networks.
In Kouvatsos, D. (ed.), Performance Modelling and Analysis of Heterogeneous Networks, pp. 371–387. River Publisher.
[8] Do, T. V., Krieger, U. R., and Chakka, R. (2008) Performance modeling of an apache web server with a dynamic pool of service processes. Telecommunication Systems,39, 117–129.
[9] Do, T. V., Papp, D., Chakka, R., and Truong, M. X. T. (2009) A Performance Model of MPLS Multipath Routing with Failures and Repairs of the LSPs. In Kou- vatsos, D. (ed.), Performance Modelling and Analysis of Heterogeneous Networks,
[10] Do, T. V. and Chakka, R. (2010) Generalised QBD processes, spectral expansion and performance modelling applications. Lecture Notes in Computer Science, volume 5233, Next Generation Internet: Performance Evaluation and Applications edited by D. D. Kouvatsos. Springer.
[11] Do, T. V. (2010) Modeling a resource contention in the management of virtual organizations. Information Sciences,180, 3108 – 3116.
[12] Do, T. V. (2010) An efficient solution to a retrial queue for the performability eval- uation of DHCP.Computers & Operations Research,37, 1191 – 1198. Algorithmic and Computational Methods in Retrial Queues.
[13] Do, T. V. and Chakka, R. (2010) Simulation and analytical approaches for esti- mating the performability of a multicast address dynamic allocation mechanism.
Simulation Modelling Practice and Theory,18, 971–983.
[14] Do, T. V. (2010) A new computational algorithm for retrial queues to cellular mobile systems with guard channels. Computers & Industrial Engineering, 59, 865 – 872.
[15] Do, T. V. and Chakka, R. (2010) A New Performability Model for Queueing and FDL-related Burst Loss in Optical Switching Nodes. Computer Communications, 33, 146–151.
[16] Do, T. V. (2011) Solution for a retrial queueing problem in cellular networks with the fractional guard channel policy. Mathematical and Computer Modelling, 53, 2058–2065.
[17] Do, T. V. (2011) Multi-Server Markov Queueing Models: Computational Algo- rithms and ICT Applications. The dissertation for the title ”DSc” of the Hungarian Academy of Sciences.
[18] Domenech-Benlloch, M. J., Gimenez-Guzman, J. M., Pla, V., Martinez-Bauset, J., and Casares-Giner, V. (2008) Generalized truncated methods for an effi- cient solution of retrial systems. Mathematical Problems in Engineering, (2008), doi:10.1155/2008/183089, 2008.
[19] Evans, R. V. (1967) Geometric Distribution in some Two-dimensional Queueing Systems. Operations Research, 15, 830–846.
[20] Falin, G. I. and Templeton, J. G. C. (1997) Retrial Queues. Chapman & Hall, London.
[21] Gail, H. R., Hantler, S. L., and Taylor, B. A. (1992) Spectral analysis of M/G/1 type Markov chains. Technical Report RC17765. IBM Research Division.
[22] Kleinrock, L. (1975)Queueing Systems. Vol I: Theory . John Wiley & Sons, Inc.
[23] Kleinrock, L. (1993) On the modeling and analysis of computer networks. Pro- ceedings of the IEEE, 81, 1179–1191.
[24] Latouche, G. and Ramaswami, V. (1999)Introduction to Matrix Analytic Methods in Stochastic Modeling. ASA-SIAM Series on Statistics and Applied Probability.
[25] Mitrani, I. and Chakka, R. (1995) Spectral expansion solution for a class of Markov models: Application and comparison with the matrix-geometric method. Perfor- mance Evaluation, 23, 241–260.
[26] Naoumov, V., Krieger, U. R., and Warner, D. (1997) Analysis of a Multi-Server Delay-Loss System With a General Markovian Arrival Process. In Chakravarthy, S. R. and Alfa, A. S. (eds.),Matrix-analytic methods in stochastic models, Septem- ber, Lecture Notes in Pure and Applied Mathematics, 183, pp. 43–66. Marcel Dekker.
[27] Neuts, M. F. (1981)Matrix Geometric Soluctions in Stochastic Model. Johns Hop- kins University Press, Baltimore.
[28] Seelen, L. P. (1986) An Algorithm for Ph/Ph/c queues. European Journal of Operational Research, 23, 118–127.
[29] Tran, H. T. (2003) Applied Methods for some Planning and Analysis Problems in Telecommunications Networking . PhD thesis Budapest University of Technology and Economics.
[30] Wallace, V. L. (1969) The Solution of Quasi Birth and Death Processes Arising from multiple Access Computer Systems. PhD thesis University of Michigan.
