A Generalized Multi-Entrance Time-Sharing Priority Queue

A generalized multi-entrance and multipriority M/G/1time-sharing system is dealt with. The system maintains manyseparate queues, each identified by two integers, the prioritylevel and the entry level The arrival process of users is ahomogenous Poisson process, while service requirements areidentically distributed and have a finite second moment. Uponarrival a user joins one of the levels, through the entry queue ofthis level. In the (n, k)-th queue, where n is thepriority level and k is the entry level, a user is eligibleto a (finite or infinite) quantum of service. If the servicerequirements of the user are satisfied during the quantum, the userdeparts, and otherwise he is trans- ferred to the end of the (n+ 1, k)-th queue for additional service. When a quantum ofservice is completed, the highest priority nonempty level is chosento be served next; within this level the queues are scannedaccording to the priority of their entry level, and the user at thehead of the highest priority nonempty queue is chosen to be served.In such a priority discipline, preferred users always get animproved service, though the service of all users is degraded inproportion to their service requirements. Expected flow times andexpected number of waiting users are derived and then specializedto the head-of-the-line M/G/1 priority discipline (in which quantahave infinite length and service is uninterrupted) and to theFBn time-sharing system. Finally, the generalizedmultientrance and multipriority time-sharing discipline is(numerically) compared with several other time-sharing systems.