Analysis of Queues with Markovian Service Processes

Abstract

Markovian service process (MSP) is a model similar to the Markovian arrival process (MAP), where arrivals are replaced with service completions. The MSP can represent various queueing models such as vacation models, N-policy models and exceptional service models. We analyze MAP/MSP/1 queues and obtain a new sort of matrix-type factorization of the vector generating function for the stationary queue length. The MAP/MSP/1 queue is a very tractable model since its behavior is represented as a quasi-birth-and-death process.

Key Words:

• Markovian service process
• Markovian arrival process, Quasi-birth-and-death process
• Queue length
• Decomposition

Mathematics Subject Classification:

• Primary 60K25
• Secondary 90B22

Acknowledgment

The author would like to thank the anonymous referees for their valuable comments.