Performance comparison of some discrete service time systems

This paper analyzes and compares the slotted time operation and the non-slotted time operation of a singleserver system with deterministic service time. These two operations are commonly used to model discrete service time systems in computer or digital communications. But due to the similarity in their operations and performance, the two models may be mixed up with each other. This paper examines by means of queueing analysis the performance of a few classes of systems that differ in the service order of their customers. The means and variances of the queue lengths, waiting times and interdeparture times of FCFS systems using the slotted time operations are first obtained from their respective LST and generating function equations. These are then used for comparison with those in non-slotted time systems. The results show that although the slotted time operation in the FCFS systems can be approximated by the non-slotted time operations under heavy traffic condition, the performances under other regions and service disciplines (e.g., the LCFS and the priority systems) may deviate significantly. They must be properly adjusted if one wishes to use the simpler equations of the non-slotted time operations to approximate the slotted time operations. The comparison graphs provided in this paper supply adjustments guidelines for the careful designers.