Abstract

Motivated by the development of complex telephone call center networks, we present a general framework for decompositions to approximately solve Markovian queueing networks with time-dependent and state-dependent transition rates. The decompositions are based on assuming either full or partial product form for the time-dependent probability vectors at each time. These decompositions reduce the number of time-dependent ordinary differential equations that must be solved. We show how special structure in the transition rates can be exploited to speed up computation. There is extra theoretical support for the decomposition approximation when the steady-state distribution of the time-homogeneous version of the model has product form.

Author Keywords: Time-dependent queues; Time-dependent queueing networks; Time-dependent Markov chains; Decomposition approximations; Systems of ordinary differential equations; Product-form queueing networks; Product-form approximations; Telephone call centers; Air traffic management

Article Outline

1. Introduction

2. The basic model

3. Telephone call center models

4. Product-form decomposition approximations

5. Special structure in the transition rates

6. The steady-state consistency check

7. Non-exponential service times and non-Poisson arrival processes

References