A Queueing Model for Business Students

In this paper we develop an N-server queueing model which overcomes some of the objections usually raised by business students when they are confronted with the discussion of queues in standard management science texts. The model permits a solution in terms of expected profit maximization rather than in terms of expected cost minimization. That is, the optimum number of servers can be determined by equating marginal cost to marginal revenue. The model has the property that the longer the waiting line the less likely it is that a new arrival will join the queue. Because of this property, the model could be called a “balking” model in the sense of Haight, (Haight, Frank A. 1957. Queueing with Balking. Biometrika 44 (3) and 4 (3) 60–369 (December); Haight, Frank A. 1960. Queueing with Balking, II. Biometrika 47 (3) and 4 285–296 (December).); would-be arrivals balk at long waiting lines. This balking has the effect of bounding the expected length of the queue so long as there are one or more servers in attendance. Finally, with this model it is possible to derive an implicit relationship between the average expenditure per customer and the value of customer waiting time.

• 저널Management Science · 8(3) · 278–286
• 토픽Advanced Queuing Theory Analysis · Management Information Systems
• DOI10.1287/mnsc.8.3.278
• 저자John S. de Cani