M/M/C queues with Markov modulated service processes

Authors:
Melike Baykal-Gursoy;Zhe Duan
Affiliations:
The State Univ. of NJ, Piscataway, NJ;The State Univ. of NJ, Piscataway, NJ
Venue:
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Year:
2006

Citing 5
Cited 1

Queueing systems with service interruptions

Operations Research
A Queueing Theory Model of Nonstationary Traffic Flow

Transportation Science
Single-Server Queue with Markov-Dependent Inter-Arrival and Service Times

Queueing Systems: Theory and Applications
Stochastic Decomposition in M/M/∞ Queues with Markov Modulated Service Rates

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On Queues with Markov Modulated Service Rates

Queueing Systems: Theory and Applications

Maintenance of infinite-server service systems subjected to random shocks

Computers and Industrial Engineering

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Abstract

Motivated by the need to study traffic flow affected by incidents we consider M/M/C queueing system where servers operate in a Markovian environment. When a traffic incident happens, either all lanes or part of a lane is closed to the traffic. As such, we model these interruptions either as complete service disruptions where none of the servers work or partial failures where all servers work at some reduced service rate. We analyze the system with multiple failure states in steady state and present a scheme to obtain the stationary number of vehicles on a link. The special case of single breakdown case is further analyzed and performance measures in closed form are obtained.