The Interrelationship Between N-policy M/G/1/K and F-policy G/M/1/K Queues with Startup Time

Abstract

This paper studies the interrelationship between the N-policy M/G/1/K queue and the F-policy G/M/1/K queue. The N- policy queuing problem investigates the most common issue of controlling service. The F- policy queuing problem deals with the most common issue of controlling arrivals. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining service time, to develop the solution algorithm for the N- policy M/G/1/K queue with startup time. We have demonstrated that the N-policy M/G/1/K queue with startup time has been effectively used to derive the solution algorithm to the F- policy G/M/1/K queue with startup time. The interrelationship between the N- policy and the F — policy queueing problems are illustrated analytically for 3-stage Erlang (service or interarrival) time distribution.

Key Words:

• F-policy
• G/M/1/K queue
• M/G/1/K queue
• N-policy
• recursive method
• startup time
• supplementary variable

Additional information

Notes on contributors

Ching-Chang Kuo

Ching-Chang Kuo received his Ph.D. degree in Industrial Engineering and Management from National Chiao Tung University, Taiwan. His research interests include queueing theory, reliability, and engineering applications.

Kuo-Hsiung Wang

Kuo-Hsiung Wang is a distinguished Professor of Business Administration at Asia University, Taiwan. He received his MA in Mathematics from the State University of New York at Buffalo, USA, and his MS and Ph.D. in Industrial and Systems Engineering from the University of Florida, Gainesville, Florida, USA. His areas of research include operations research, queueing theory, reliability, and stochastic modelling. His publications appeared in Microelectronics and Reliability, Omega, Naval Research Logistics, Journal of the Operational Research Society, European Journal of Operational Research, Computers and Operations Research, Computers and Industrial Engineering, Applied Mathematical Modelling, Mathematical Methods of Operations Research, Applied Mathematics and Computation, Journal of Computational and Applied Mathematics, and others.

W. L. Pearn

W. L. Pearn is a Professor of Industrial Engineering and Management at National Chiao Tung University, Taiwan. He received his Ph.D. degree in operations from the University of Maryland, College Park, Maryland, USA. He has worked at AT&T Bell Laboratories as a quality research staff before joining National Chiao Tung University. His research interests include process capability, network optimization, and production management. His publications appeared in Journal of the Royal Statistical Society, Series C, Journal of Quality Technology, Journal of Applied Statistics, Statistics and Probability Letters, Quality and Quantity, Metrika, Statistics, Omega, Journal of the Operational Research Society, European Journal of Operational Research, Operations Research Letters, Networks, International Journal of Productions Research, and others.