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Steady-state analysis of shortest expected delay routing

We consider a queueing system consisting of two nonidentical exponential servers, where each server has its own dedicated queue and serves the customers in that queue FCFS. Customers arrive according to a Poisson process and join the queue promising the shortest expected delay, which is a natural and near-optimal policy for systems with nonidentical servers. This system can be...

Two perishable inventory systems with one-way substitution

Motivated by the ABO issue of the blood bank system, in which the portions stored have constant shelf life, we consider two subsystems of perishable inventory. The two Perishable Inventory Subsystems-PIS A and PIS B, are correlated to each other through a one-way substitution of demands. Specifically, the input streams and the demand streams applied to each subsystem are four...

Joint queue length distribution of multi-class, single-server queues with preemptive priorities

In this paper we analyze an M/M/1 queueing system with an arbitrary number of customer classes, with class-dependent exponential service rates and preemptive priorities between classes. The queuing system can be described by a multi-dimensional Markov process, where the coordinates keep track of the number of customers of each class in the system. Based on matrix-analytic...

A product form solution to a system with multi-type jobs and multi-type servers

We consider a memoryless single station service system with servers \(\mathcal{S}=\{m_{1},\ldots,m_{K}\}\), and with job types \(\mathcal{C}=\{a,b,\ldots\}\). Service is skill-based, so that server m i can serve a subset of job types \(\mathcal{C}(m_{i})\). Waiting jobs are served on a first-come-first-served basis, while arriving jobs that find several idle servers are assigned...

Inventory rationing for a system with heterogeneous customer classes

business problems. Application areas include natural resources, inventory management, computer systems, and ambulance routing. Ivo Adan received the M.Sc. and Ph.D. degrees in Mathematics from the Eindhoven ... Research and Probability in the Engineering and Informational Sciences. Ivo Adan is a senior fellow of the European research institute Eurandom. His current research interests are in the modeling and design

Synchronized reneging in queueing systems with vacations

Ivo Adan iadan@win.tue.nl 0 Antonis Economou 0 Stella Kapodistria 0 0 I. Adan ( ) Department of Mathematics and Computer Science, Technische Universiteit Eindhoven , P.O. Box 513, 5600 MB Eindhoven

Exact asymptotics for the stationary distribution of a Markov chain: a production model

We derive rough and exact asymptotic expressions for the stationary distribution π of a Markov chain arising in a queueing/production context. The approach we develop can also handle “cascades,” which are situations where the fluid limit of the large deviation path from the origin to the increasingly rare event is nonlinear. Our approach considers a process that starts at the...

Analysis of a tandem network model of a single-router Network-on-Chip

We study a single-router Network-on-Chip modelled as a tandem queueing network. The first node is a geo K /D/1 queue (K fixed) representing a network interface, and the second node is a ./G/1 queue representing the packet switch. If K>1 we have train arrivals at the second node. If K=1 the arrival process of the second node reduces to a Bernoulli process. In the latter case...

On a generic class of two-node queueing systems

This paper analyzes a generic class of two-node queueing systems. A first queue is fed by an on–off Markov fluid source; the input of a second queue is a function of the state of the Markov fluid source as well, but now also of the first queue being empty or not. This model covers the classical two-node tandem queue and the two-class priority queue as special cases. Relying...

Patient mix optimisation and stochastic resource requirements: A case study in cardiothoracic surgery planning

Cardiothoracic surgery planning involves different resources such as operating theatre time, beds, IC beds and nursing staff. In the daily practice of the Thorax Centre case study setting, the planning focuses on optimal use of operating theatre time, though the performance of the Thorax Centre as a whole is often more limited by other resources. For operating theatres a master...