Optimal Management of a Removable and Non-Reliable Server in an Infinite and a Finite M/H_k/1 Queueing System

Abstract

We consider a single removable and non-reliable server in both infinite capacity and finite capacity queueing systems with Poisson arrivals and ¿-type hyper-exponential distribution for the service times operating under the N policy. The server may be turned on at arrival epochs or off at departure epochs. Breakdown and repair times of the server are assumed to follow a negative exponential distribution. Cost model for infinite capacity queueing system (say cost model 1) is developed to determine the optimal operating policy. Cost model for finite capacity queueing system (say cost model 2) is developed to determine the optimal operating policy and the optimal system capacity, simultaneously. This paper presents the optimal operating policy, the optimal system capacity, the minimum expected cost based on specific values given to the system parameters, as well as to the cost elements. The sensitivity analysis is also investigated.

Key Words:

• Management
• k-type hyper-exponential distribution
• non-reliable server
• queue

Additional information

Notes on contributors

Kuo-Hsiung Wang

Kuo-Hsiung Wang Professor of Applied Mathematics at National Chung-Hsing University, Taiwan. He received his MA in Mathematics from the State University of New York at Buffalo, USA, and MS and Ph.D. degrees in Industrial and Systems Engineering from the University of Florida, USA. His research interests include operations research, queueing theory, reliability, and stochastic modeling.

Hung-Ting Kao

Hung-Ting Kao Received his MS degree from the Department of Applied Mathematics at National Chung-Hsing University, Taiwan. His research interests include statistics, and queueing theory.

Gang Chen

Gang Chen Process Design Engineer at Bank of America, Dallas, Texas, USA. He received his Ph.D. degree in operations research from the Department of Industrial and Systems Engineering at University of Florida, USA. His areas of research include stochastic modeling and analysis, combinatorial optimization, and simulation modeling.