Summary: Stochastic Processes and their Applications 22 (1986) 291-313
SOME INTERESTING PROCESSES ARISING AS HEAVY
TRAFFIC LIMITS IN AN M/M/co STORAGE PROCESS
Department of Statistics, University of California, Berkeley, CA 94720, USA
Received 13 August 1985
Revised 28 March 1986
Recent works by Newell  and Coffman et al.  have studied a queuing or storage model
which is most easily visualized as the process of parking cars in a parking lot where customers
park as close as they can to some fixed point. This paper describes several space-time processes
which arise as heavy-traffic limits in this model, and which seem interesting in their own right.
M/M/a queue * dynamic storage allocation * heavy-traffic * infinite-dimensional diffusion * ex-
tremal properties of stationary processes
Imagine a supermarket with a parking lot with parking spaces labeled 1,2, 3,. . . .
A simple and natural model for the arrival, parking and eventual departure of cars
is the following.
(a) Cars arrive as a Poisson process of rate A.