The design of the UNIX operating system
The design of the UNIX operating system
Modelling of computer and communication systems
Modelling of computer and communication systems
Synchronization with eventcounts and sequencers
Communications of the ACM
Operating System Concepts
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
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We consider a queueing system where the servers are arranged in a circle, and each arriving customer requires a pair of resources that is shared by its server with the respective neighbors on either side. If either resource is being used, the customer is denied service. Customers arrive at each server according to independent Poisson processes, and lengths of service times at each server have an exponential distribution. We derive a closed-form formula for the expected fraction of busy servers at any time in terms of the number of servers and the utilization factor (defined as the arrival rate times the mean service-time duration). This allows us to evaluate system performance when these parameters are varied, and to determine whether denying service to arrivals at alternate servers improves performance. We relate the system to Dijkstra’s dining philosophers problem, which is an abstraction for resource sharing in an operating system.