Wireless Personal Communications (2006) 39: 135–149 DOI: 10.1007/s11277-006-9083-0 C  Springer 2006 Performance of Queueing Model of one UMTS Cell with R Virtual Zones by the Maximum Entropy Solution AYMEN I. ZREIKAT Faculty of Science, Information Technology Department, Mutah University, P.O. Box 7, (61710), Mutah-Karak-Jordan E-mail: aymen@mutah.edu.jo Abstract. UMTS stands for Universal Mobile Telecommunications System, which is one of the third generation (i.e., 3G) cellular systems, will come into full commercial phase by year 2005 and the first UMTS services are launched commercially in 2001. Therefore, the research of UMTS is an important and urgent task. In this paper, the performance of UMTS systems is studied through a queueing model which consists of one UMTS with many virtual zones to evaluate the system uplink traffic performance. The two performance measures: blocking probability and system utilization are obtained by the Maximum Entropy Principle, i.e., ME solutions for S R×R (GGeo/GGeo/1)/ N queue. S R×R (GGeo/GGeo/1)/ N system means that arrival time and service time are both GGeo (Generalized Geometric) distributed, each output port has a single server and the maximum capacity is N . After the theoretical analysis, the numerical results are found for the idiographic example, S 8×8 (GGeo/GGeo/1)/512 queueing model. Additionally, the performance of this queueing model is discussed with the effect of the parameters Ca 2 (squared coefficient of variation of the interarrival time), Cs 2 (squared coefficient of variation of the service time) and the arrival rate, λ. Keywords: performance evaluation, queueing theory, UMTS, maximum entropy, wireless mobile networks 1. Introduction The introduction of UMTS (Universal Mobile Telecommunication System) as a standard for third generation of mobile networks promises circuit and Packet switched mobile access with fair data rates. In addition to the traditional voice communication, this system enables a wide range of new data services including mobile internet and multimedia [1]. It is not yet clear, however, how this service mix will look like in real UMTS systems and therefore, it is difficult for network providers to forecast the actual system capacity [2]. The UMTS standardization bodies have designed a radio interface highly flexible able to provide different bearer services with different bit rates and different transfer modes [1–3]. The evaluation of the performance of the UMTS radio access network is widely discussed in the literature in the uplink as well as the downlink [4–8]. However, in this paper, the performance of the uplink UMTS is studied using the maximum entropy solution. In the field of system modeling, expected values of various performance distributions of interest, such as the number of jobs in each resource queue concerned, are often known, or may be explicitly derived, in terms of moments of interarrival and service time distributions. Note that the determination of the distributions themselves, via classical queuing theory, may prove an infeasible task even for system of queues with moderate complexity. Hence, it is implied that the method of entropy maximization may be applied to characterize useful information theo- retic approximations of performance distributions of queuing systems and networks. Focusing