SOCIAL OPTIMIZATION VERSUS SELF-OPTIMIZATION IN WAITING LINES

Abstract

A queueing model is considered where customers arriving in a Poisson stream are given the choice of either joining the waiting line or - by declining to do so - of foregoing the benefits accruing through service. The decision of each customer is based on his concrete benefit-cost analysis. As his service time is constant, and exhaustive information as to the actual state of the system is available, both of the alternatives presented to the individual customer are completely deterministic and his decision is not reached under uncertainty or risk. The cost structure envisaged as well as additional assumptions give rise to a queueing model with limited waiting room. A number of simple and comprehensive optimization equations are derived.

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