M/M/C queues with Markov modulated service processes

Melike  Baykal-Gursoy; Zhe  Duan

1st International ICST Conference on Performance Evaluation Methodologies and Tools

Research Article

M/M/C queues with Markov modulated service processes

Cite: BibTeX Plain Text

@INPROCEEDINGS{10.1145/1190095.1190143,
    author={Melike  Baykal-Gursoy and Zhe  Duan},
    title={M/M/C queues with Markov modulated service processes},
    proceedings={1st International ICST Conference on Performance Evaluation Methodologies and Tools},
    publisher={ACM},
    proceedings_a={VALUETOOLS},
    year={2012},
    month={4},
    keywords={},
    doi={10.1145/1190095.1190143}
}

Melike Baykal-Gursoy
Zhe Duan
Year: 2012
M/M/C queues with Markov modulated service processes
VALUETOOLS
ACM
DOI: 10.1145/1190095.1190143

Melike Baykal-Gursoy¹^,*, Zhe Duan¹^,*

1: Industrial and Systems Eng. Rutgers, The State Univ. of NJ 96 Frelinghuysen Rd Piscataway, NJ 08854-8018

*Contact email: gursoy@rci.rutgers.edu, zheduan@eden.rutgers.edu

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.

Published: 2012-04-12
Publisher: ACM

: http://dx.doi.org/10.1145/1190095.1190143