a study of optimal dimensioning of queues with respect to social and individual profit

in this paper, a system of gig/l/k queue is considered. the optimal system's capacity (k), when the system is optimized with respect to the benefit of the entire system (social optimization) and when the criterion for optimality is individual gains (individual optimization), is determined and compared. in social optimization, the system capacity is obtained through maximization of the system's profit. however, when individual gains is the criteria, the system capacity is determined as a result of customers not joining the system because they estimate that getting service from the system does not yield them any profit and therefore leave the system. it is shown by simulation that irrespective of the traffic intensity, p and arrival and service time distributions with different failure and acceleration rates, the k obtained from social optimization of the system is always equal or less than the k obtained from individual optimization. thus, the social optimization of the system not only maximizes the system's profit but also preserves individual gains and prevents the customer from leaving the system. in this paper, some other interesting results are also reported.