Workloads and waiting times in single-server systems with multiple customer classes

One of the most fundamental properties that single-server multi-class service systems may possess is the property of work conservation. Under certain restrictions, the work conservation property gives rise to a conservation law for mean waiting times, i.e., a linear relation between the mean waiting times of the various classes of customers. This paper is devoted to single-server multi-class service systems in which work conservation is violated in the sense that the server's activities may be interrupted although work is still present. For a large class of such systems with interruptions, a decomposition of the amount of work into two independent components is obtained; one of these components is the amount of work in the corresponding systemwithout interruptions. The work decomposition gives rise to a (pseudo)conservation law for mean waiting times, just as work conservation did for the system without interruptions

Optimization of Polling Systems and Dynamic Vehicle Routing Problems on Networks

We consider the problem of optimizing a polling system, i.e., of optimally sequencing a server in a multi-class queueing system with switch-over times in order to minimize a linear objective function of the waiting times. The problem has important applications in computer, communication, production and transportation networks. We propose nonlinear programming relaxations that provide strong lower bounds to the optimal cost for all static policies. We also obtain lower bounds for dynamic policies as well, which are primarily useful under light traffic conditions and/or small switch-over times. We conjecture that the lower bounds developed in this paper for the class of static policies are also valid for dynamic policies under heavy traffic conditions. We use the information from the lower bound and integer programming techniques to construct static policies that are very close (0-3%) to the lower bounds. We compare numerically our proposed policies with static policies proposed in the literature as well as with dynamic policies and find that the policies we propose outperform all static policies proposed in the literature and at least in heavier traffic outperform dynamic policies as well

Analysis of a polling system modeling QoS differentiation in WLANs

This paper investigates a polling system with a random polling scheme, a 1-limited service discipline and deterministic service requirement modeling WLANs with QoS differentation capability. The system contains high and low priority queues that are distinguished via the probability of being served next. We propose a new iteration algorithm to approximate the waiting time of customers in the high and low priority queues. As shown by simulation results, our approximation is accurate for light to moderately loaded networks

Waiting times in a two-queue model with exhaustive and Bernoulli service

Network Analysis;operations research

Waiting time estimates in symmetric ATM-oriented rings with the destination release of used slots

This paper considers the basic access mechanism in asynchronous transfer mode (ATM)-oriented rings which, like Orwell, ATM ring, and ALine, apply destination release of used slots. The released slots may be reused by the destination station, or in some protocols, they must be given to the next station. Such a mechanism can be modeled by a multiple-server multiqueue system, where switchover times between consecutive polling instants of the queues are nonzero. The server polls the queues according to a certain polling discipline, which is dependent on the service time. This paper presents approximate mean minipacket waiting times in such systems. The approximation is based on a polling queueing model with Markovian server routing. Poisson arrivals and a symmetric workload model for minipackets having a full and partial traffic matrix are assumed. The performance characteristics are compared between the alternative option