We consider multiprocessing systems where processes make independent, Poisson distributed resource requests with mean arrival time 1. We assume that resources are not released. It is shown that the expected deadlock time is never less than 1, no matter how many processes and resources are in the system. Also, the expected number of processes blocked 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 efficiency in terms of Abel sums. We derive asymptotic expressions for these statictics in the case of systems with many processes and the case of systems with a fixed number of processes. In the latter, generalizations of the Ramanujan Q-function arise. We use singularity analysis to obtain asymptotics of coefficients of generalized Q-functions.