SOCIAL OPTIMIZATION VERSUS SELF-OPTIMIZATION IN WAITING LINES

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. Since 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. After detailed analysis of the model and blending with the cost structure it is shown that the criterion for self-optimization of the customer will not bring about social optimization, the latter being defined as the maximally feasible expected net gain per unit time accruing to the totality of customers. A number of simple and comprehensive optimization equations are derived. By marginal analysis the correctness of the simple equations is verified and their applicability is extended to models possessing more general character.