EXPECTED DEADLOCK TIME IN A MULTIPROCESSING SYSTEM

We consider multiprocessing systems where processes make independent, Poisson distributed resource requests with mean arrival time 1. We ass ume that resources are not released. It is shown that the expected dea dlock time is never less than 1, no matter how many processes and reso urces are in the system. Also, the expected number of processes blocke d by deadlock time is one-half more than half the number of initially active processes. We obtain expressions for system statistics such as expected deadlock time, expected total processing time, and system eff iciency, in terms of Abel sums. We derive asymptotic expressions for t hese statistics in the case of systems with many processes and the cas e of systems with a fixed number of processes. In the latter, generali zations of the Ramanujan Q-function arise. We use singularity analysis to obtain asymptotics of coefficients of generalized Q-functions.