An Optimal Waiting Policy in a System of Multiple Queues with the Shortest Queue Discipline

Abstract

A system with several queues is considered. Each queue has a server with exponential service time with same service rate. Normal customers arrive at the system and choose which queue to join. They are supposed to join the shortest queue. Special customers also arrive at the system though the arrivals are rare. They can also choose which queue to join and they have other options, waiting in the room for them and leaving the system. This paper deals with the optimal policy of the special customers. It is shown that the optimal policy has monotone properties.

Key Words:

• Markov decision process
• multiple queues
• waiting policy

Additional information

Notes on contributors

Koyanagi Junji

Junji Koyanagi received the M.E. and Ph.D. of Informatics degrees from Kyoto University, Japan, in 1990 and 2001, respectively. In 1990 he joined the Tottori University as an Assistant Professor, and is now working as an Associate Professor in the department of Management of Social Systems and Civil Engineering in Graduate School of Tottori University. His research areas include Queueing System Control and Reliability. He is a regular member of ORSJ and JSIAM.

Kawai Hajime

Hajime Kawai received the M.E. and Ph.D. of Engineering degrees from Kyoto University, Japan, in 1971 and 1979, respectively. In 1973 he joined the Kyoto University as an Assistant Professor, then worked in Osaka Prefecture University from 1983 to 1986. From 1987, he is a Professor in Tottori University, now, in the department of Management of Social Systems and Civil Engineering in Graduate School of Tottori University. His research areas include Markov Decision Process and Reliability. He is a regular member of ORSJ and IEICE.