Paper Info
Title
Multi-threshold policy for a multi-server queue with synchronous single vacation
Abstract
This paper considers an infinite buffer M/M/c queueing system in which servers follow a multi-threshold vacation policy. With such a policy, at a service completion instant, if the number of customers in the system is less than a prefixed threshold value, part of servers together take a single vacation (or leave for a random amount of time doing other secondary job). At the vacation completion instant, they return to the system for serving the customers. Some practical production and inventory systems or call centers could be modeled as this Markovian queue with a multi-threshold vacation policy. Using the Markovian process model, we obtain the exact closed-form expression of rate matrix and the stationary distribution of the number of customers in the system. A cost model is developed to search the joint optimal values of the thresholds of vacation policy and service rate of each server, which minimizes the long-term average cost. Some numerical results are presented to illustrate the optimization procedures.
Year
DOI
Venue
2013
10.1016/j.mcm.2012.10.012
Mathematical and Computer Modelling
Keywords
Field
DocType
m/m/c queue,multiple-threshold,synchronous single vacation,m m c queue
M/M/1 queue,D/M/1 queue,Mathematical optimization,M/D/1 queue,M/M/c queue,Computer science,M/G/1 queue,M/G/k queue,M/D/c queue,M/M/∞ queue
Journal
Volume
Issue
ISSN
57
5-6
0895-7177
Citations 
PageRank 
References 
1
0.36
14
Authors
2
Name
Order
Citations
PageRank
Chia-Huang Wu16211.61
Jau-Chuan Ke234844.17