Exploring a new Markov chain model for multiqueue systems.

Traditionally, Markov models have been used to study multiserver systems using exhaustive or gated service. In addition, exhaustive-limited and gate-limited models have also been used in communication systems to reduce overall latency. Recently the authors have proposed a new Markov Chain approach to study gate-limited service. Multiqueue systems such as polling systems, in which the server serves various queues have also been extensively studied but as a separate branch of queueing theory. This paper proposes to describe multiqueue systems in terms of a new Markov Chain called the Zero-Server Markov Chain (ZSMC). The model is used to derive a formula for the waiting times in an exhaustive polling system. An intuitive result is obtained and this is used to develop an appoximate method which works well over normal operational ranges

Iterative approximation of k-limited polling systems

The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) k-limited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logistics. Knowledge of the queue length distributions is needed to operate the system properly. The multi-queue polling system is decomposed into single-queue vacation systems with k-limited service and state-dependent vacations, for which the vacation distributions are computed in an iterative approximate manner. These vacation models are analyzed via matrix-analytic techniques. The accuracy of the approximation scheme is verified by means of an extensive simulation study. The developed approximation turns out be accurate, robust and computationally efficient

On the Modelling of the Mobile WiMAX (IEEE 802.16e) Uplink Scheduler

Packet scheduling has drawn a great deal of attention in the field of wireless networks as it plays an important role in distributing shared resources in a network. The process involves allocating the bandwidth among users and determining their transmission order. In this paper an uplink (UL) scheduling algorithm for the Mobile Worldwide Interoperability for Microwave Access (WiMAX) network based on the cyclic polling model is proposed. The model in this study consists of five queues (UGS, ertPS, rtPS, nrtPS, and BE) visited by a single server. A threshold policy is imposed to the nrtPS queue to ensure that the delay constraint of real time traffic (UGS, ertPS, and rtPS) is not violated making this approach original in comparison to the existing contributions. A mathematical model is formulated for the weighted sum of the mean waiting time of each individual queues based on the pseudo-conservation law. The results of the analysis are useful in obtaining or testing approximation for individual mean waiting time especially when queues are asymmetric (where each queue may have different stochastic characteristic such as arrival rate and service time distribution) and when their number is large (more than 2 queues)

Monotonicity and stability of periodic polling models

Polling Systems;Stability;operations research