Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 857871, 23 pages
Research Article

Maintenance in Single-Server Queues: A Game-Theoretic Approach

Department of Mathematical Sciences, College of Science, Florida Institute of Technology, Melbourne, FL 32901, USA

Received 18 August 2009; Accepted 27 November 2009

Academic Editor: Alexander P. Seyranian

Copyright © 2009 Najeeb Al-Matar and Jewgeni H. Dshalalow. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We use antagonistic stochastic games and fluctuation analysis to examine a single-server queue with bulk input and secondary work during server's multiple vacations. When the buffer contents become exhausted the server leaves the system to perform some diagnostic service of a minimum of L jobs clustered in packets of random sizes (event A). The server is not supposed to stay longer than T units of time (event B). The server returns to the system when A or B occurs, whichever comes first. On the other hand, he may not break service of a packet in a middle even if A or B occurs. Furthermore, the server waits for batches of customers to arrive if upon his return the queue is still empty. We obtain a compact and explicit form functional for the queueing process in equilibrium.