IJE TRANSACTIONS B: Applications Vol. 17, No. 3 (October 2004) 289-298   

downloaded Downloaded: 44   viewed Viewed: 1450

R. Tavakkoli-Moghaddam

Department of Industrial Engineering, Faculty of Engineering
University of Tehran, Tehran, Iran, tavakoli@ut.ac.ir

A. Azaron

Department of Industrial Engineering, Faculty of Engineering
Bu-Ali Sina University, Hamadan, Iran, aazaron@dal.ca

L. Mehrad-Pay

Department of Industrial Engineering, Mazandaran University of Science and Technology
Babol, Iran, Laleh_mp@yahoo.com
( Received: February 05, 2003 – Accepted in Revised Form: June 10, 2004 )

Abstract    The purpose of this paper is to analyze the effect of a particular control doctrine applied to the service mechanism of a queuing process with lapse. It is assumed that the service discipline is FCFS (first come, first served), arrival process is Poisson, service time distribution is exponential, service process is one phase and the capacity is infinite. It is also assumed that the customer may give up joining the system when the queue is overcrowded. Expressions are obtained for queue length probabilities for describing control performance. The aim of which is to decrease customer’s expectancy time via incorporation of a service cost structure. The model is executed by two control methods, namely the single level control and double level hysteretic control. Finally, the results are compared with each other through solving a numerical example.


Keywords    Queuing Systems with Lapse, Optimal Control, Single Level, Double Level, Hysteretic Controls



1. Hiller, F. S. and Lieberman, G. J., “Introduction to Operations Research”, 6th Ed., McGraw-Hill Co., NY, (1995).

2. Dilworth, J. B., “Production and Operations Management”, Manufacturing and Services, 5th Ed., McGraw-Hill Co., (1993).

3. Stidham, S., “L = λW: A Discounted Analogue and A New Proof”, Oper. Res., Vol. 20, (1972), 1115-1126.

4. Crabill, T. B., “A Classified Bibliography of Research on Optimal Design and Control of Queues”, Oper. Res., Vol. 25, (1976), 219-232.

5. Yadin, M. and Naor, P., “On Queuing Systems with Variable Service Capacities”, Nav. Res. Log. Quart., Vol. 14, (1967), 43-54.

6. Gebhardt, T., “A Queuing Process with Bi-Level Hysteretic Service Rate Control”, Nav. Res. Log. Quart., Vol. 14, (1967), 55-68.

7. Sobel, M. J., “Optimal average-cost policy for a queue with start-up and shut-down costs”, Oper. Res., Vol. 17, (1968), 145-162.

8. Crabill, “Optimal control of a maintenance system with variable service rates”, (1972), 736-745.

9. Wolf, “The Optimal of service in a tandem queues”, Permamente Services, (1973), 824-831.

10. Chao, X., “Triggered Concurrent Batch Arrivals and Batch Departures in Queuing Networks”, Theory and Applications, Vol. 10, (2000), 115-129.

11. Crabill, T. B., “Optimal Control of A Service Facility with Variable Exponential Service Times and Constant Arrival Rate”, Manage. Sci., Vol. 18, (1972), 560-566.

12. Tijms, H., “A Control Policy for A Priority Queue with Removable Server”, Mathematisch Centrum, (1973), 833-837.

International Journal of Engineering
E-mail: office@ije.ir
Web Site: http://www.ije.ir