Queueing Systems

, Volume 51, Issue 1–2, pp 173–186 | Cite as

On the Three Threshold Policy in the Multi-Server Queueing System with Vacations



In this paper, we study an M/M/c queue with a three threshold vacation policy denoted by (e, d, N). With such a policy, the servers keep serving the customers until the number of idle servers reaches d and then e of d servers start taking a vacation together. These e servers keep taking vacations until the number of customers in the system is at least N at a vacation completion instant, then the e servers return to serve the queue again. Using the matrix analytic method, we obtain the stationary performance measures and prove the conditional stochastic decomposition properties for the waiting time and queue length. This model is a generalization of previous multi-server vacation models and offers a useful performance evaluation and system design tool in multi-task server queueing systems.


M/M/c queue vacation model threshold policy quasi-birth and death process matrix geometric solutions conditional stochastic decomposition 


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Decision Sciences, College of Business and EconomicsWestern Washington UniversityBellinghamUSA

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