A simple and accurate analysis for performance evaluation and comparison of a class of queueing schemes for priority handoff and call admission control in micro-cellular PCNs presented. The analytical model is developed based on a birth-death process with state-dependent Poisson arrivals, exponentially distributed and decomposed service-time, multiple servers, finite or infinite system capacity and general customer impatience until the beginning of service. The measures of interests include the probabilities of handoff forced terminations, handoff failure and new call blocking. The closed-form solutions are obtained and numerical results are presented for important modeling scenarios. This analysis is believed to have significant uses for network planning and performance optimization.

Queueing Systems - Vol. 1: Theory

An analytical modeling for a class of queueing priority handoff and call admission control schemes in micro-cellular PCNs

The behavior of single server queuing systems is characterized by various “performance distributions”, including distributions of queue length, waiting time, residence time, busy period, number served in a busy period, etc In principle, if the arrival and service time distributions are known exactly, then these performance distributions can be computed using standard techniques We consider the problem of estimating the distributions when only the first few moments of the service time distribution are known Our approach uses standard relations to compute moments of the performance distributions from the known moments of the service time distribution and the principles of maximum entropy and minimum cross-entropy to estimate the performance distributions themselves For M/G/1 systems with known average arrival rates, we derive analytic results for cases when one or two moments of the service time distribution are known, and we show how one can compute results using as many moments of the service time distribution as are available For G/G/1 systems, our results are limited to the case in which only the average arrival and service rates are known Among the results obtained with this information theoretic approach is a new light-load approximation for the M/M/1 busy period probability density Throughout the paper, we illustrate our approach using M/M/1, M/H2/1, and M/D/1 examples

http://link.springer.com/content/pdf/10.1007%2F978-94-009-9062-3_42.pdf

Information Theoretic Approximations for M/G/1 Queuing Systems

Fork-join systems play a pivotal role in the analysis of distributed systems, telecommunication infrastructures, and storage systems. In this article, we consider a fork-join system consisting of K parallel servers, each of which works on one of the K tasks that form each job. The system allocates a fixed amount of computational resources among the K servers, hence determining their service speed. The goal of this article is that of studying the resource allocation policies among the servers. We assume that the queueing disciplines of the fork- and join-queues are First Come First Served. At each epoch, at most K tasks are in service while the others wait in the fork-queues. We propose an algorithm with a very simple implementation that allocates the computational resources in a way that aims at minimizing the join-queue lengths, and hence at reducing the expected job service time. We study its performance in saturation and under exponential service time. The model has an elegant closed-form stationary distribution. Moreover, we provide an algorithm to numerically or symbolically derive the marginal probabilities for the join-queue lengths. Therefore, the expressions for the expected join-queue length and the expected response time under immediate join can be derived. Finally, we compare the performance of the proposed resource allocation algorithm with that of other strategies.

background

Dynamic Resource Allocation in Fork-Join Queues

Eine Lagerzielmengenpolitik fur den Fall intermittierender Fertigung mehrerer Sorten auf einer Anlage bei stochastischer Nachfrage wird durch ein Warteschlangenmodell abgebildet. Fur die sich ergebenden Kostenfunktion wird eine Approximation vorgeschlagen. Die Bestimmung optimaler Losgrosen und Lagerzielmengen wird untersucht.

/pdf/eine-produktions-lagerhaltungspolitik-bei-stochastischer-1i5kw7thpa.pdf

Eine Produktions-/Lagerhaltungspolitik bei stochastischer Nachfrage im Mehrproduktfall

In this work the mathematical model of transactions processing systems is described. For this model we propose a procedure of transformation of initial system, which makes it possible to calculate the lower bound of average transaction processing delay numerically. A few ways of the bound tightening are also discussed.

Queueing Systems - Vol. 1: Theory

Citations

An analytical modeling for a class of queueing priority handoff and call admission control schemes in micro-cellular PCNs

Information Theoretic Approximations for M/G/1 Queuing Systems

Dynamic Resource Allocation in Fork-Join Queues

Eine Produktions-/Lagerhaltungspolitik bei stochastischer Nachfrage im Mehrproduktfall

Lower bound for average delay in transactions processing systems

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