Analysis of a batch-service queue with variable service capacity, correlated customer types and generally distributed class-dependent service times

Queueing models with batch service have been studied frequently, for instance in the domain of telecommunications or manufacturing. Although the batch server's capacity may be variable in practice, only a few authors have included variable capacity in their models. We analyse a batch server with multiple customer classes and a variable service capacity that depends on both the number of waiting customers and their classes. The service times are generally distributed and class-dependent. These features complicate the analysis in a non-trivial way. We tackle it by examining the system state at embedded points, and studying the resulting Markov Chain. We first establish the joint probability generating function (pgf) of the service capacity and the number of customers left behind in the queue immediately after service initiation epochs. From this joint pgf, we extract the pgf for the number of customers in the queue and in the system respectively at service initiation epochs and departure epochs, and the pgf of the actual server capacity. Combined with additional techniques, we also obtain the pgf of the queue and system content at customer arrival epochs and random slot boundaries, and the pgf of the delay of a random customer. In the numerical experiments, we focus on the impact of correlation between the classes of consecutive customers, and on the influence of different service time distributions on the system performance. (C) 2019 Elsevier B.V. All rights reserved

Lattice path counting and the theory of queues

In this paper we will show how recent advances in the combinatorics of lattice paths can be applied to solve interesting and nontrivial problems in the theory of queues. The problems we discuss range from classical ones like M^a/M^b/1 systems to open tandem systems with and without global blocking and to queueing models that are related to random walks in a quarter plane like the Flatto-Hahn model or systems with preemptive priorities. (author´s abstract)Series: Research Report Series / Department of Statistics and Mathematic

Performance analysis of priority queueing systems in discrete time

The integration of different types of traffic in packet-based networks spawns the need for traffic differentiation. In this tutorial paper, we present some analytical techniques to tackle discrete-time queueing systems with priority scheduling. We investigate both preemptive (resume and repeat) and non-preemptive priority scheduling disciplines. Two classes of traffic are considered, high-priority and low-priority traffic, which both generate variable-length packets. A probability generating functions approach leads to performance measures such as moments of system contents and packet delays of both classes

Reflections on queue modelling from the last 50 years

Queueing theory continues to be one of the most researched areas of operational research, and has generated numerous review papers over the years. The phrase 'queue modelling' is used in the title to indicate a more practical emphasis. This paper uses work taken predominantly from the last 50 years of pages of the Operational Research Quarterly and the Journal of the Operational Research Society to offer a commentary on attempts of operational researchers to tackle real queueing problems, and on research foci past and future. A new discipline of 'queue modelling' is proposed, drawing upon the combined strengths of analytic and simulation approaches with the responsibility to derive meaningful insights for managers

A methodological approach to BISDN signalling performance

Sophisticated signalling protocols are required to properly handle the complex multimedia, multiparty services supported by the forthcoming BISDN. The implementation feasibility of these protocols should be evaluated during their design phase, so that possible performance bottlenecks are identified and removed. In this paper we present a methodology for evaluating the performance of BISDN signalling systems under design. New performance parameters are introduced and their network-dependent values are extracted through a message flow model which has the capability to describe the impact of call and bearer control separation on the signalling performance. Signalling protocols are modelled through a modular decomposition of the seven OSI layers including the service user to three submodels. The workload model is user descriptive in the sense that it does not approximate the direct input traffic required for evaluating the performance of a layer protocol; instead, through a multi-level approach, it describes the actual implications of user signalling activity for the general signalling traffic. The signalling protocol model is derived from the global functional model of the signalling protocols and information flows using a network of queues incorporating synchronization and dependency functions. The same queueing approach is followed for the signalling transfer network which is used to define processing speed and signalling bandwidth requirements and to identify possible performance bottlenecks stemming from the realization of the related protocols

Discrete Time Analysis of Multi-Queue Systems with Multiple Departure Streams in Material Handling and Production under Different Service Rules

In this work, we present a modelling approach in order to depict service rules holistically. The developed model is called multi-queue system with multiple departure streams (MQSMDS). The MQSMDS is modelled as a discrete time Markov chain. On the basis of a numerical study, the system characteristics are evaluated. The results of this work enable a rapid and low-cost analysis of material handling and production systems as well as a fast and easy identification of suitable service rules