An N-Server Stochastic Service System with Customer Preferences

The Erlang loss formula is currently used to estimate the capacity of a set of N linear curb spaces for vehicle parking; but this model applies only if drivers will accept the first vacant space they come to, a condition not found in practice. This paper develops a model of service that permits customers to decline an available server (space) when the walking distance would be excessive. The results enable the calculation of not only the overall loss, but the ability of the service system to satisfy customer preferences. It evaluates the conditional loss (given the space preferred), the access time, and the expected walking distance for each preference class. We give some examples of results based upon traffic characteristics forecast at a large, modern air terminal. It is found that the Erlang formula considerably underestimates the space requirements for linear curb parking and ignores the impact of its driver-indifference assumption upon passenger walking distance. The model has been programmed in APL for rapid calculations of all pertinent factors, allowing economical interactive use for planning—a curb with 30 spaces can be evaluated in approximately 1/2 second of CPU time.