Multi-server threshold queues with hysteresis

A queueing system with K servers operates in the following manner. When the system is empty, arriving customers are attended by only one server. A set of forward threshold values is defined so that at epochs at which the number of customers in the system exceeds a forward threshold value an extra server is added. Similarly, a set of reverse threshold values is defined so that at epochs at which the number of customers in the system becomes less than a reverse threshold value one server is removed. The forward and reverse threshold values are assumed to be different. Closed-form occupancy distribution and mean delay of customers in the system are obtained by the Green's function method.     

A distributed Poisson approximation for preempt-resume clockedschedules

Many telecommunication systems with time-critical requirements use a preempt-resume clocked schedule. An approximation to the ergodic distribution of the time to completion of a low-priority task is obtained by treating the priority service time distribution as the limit of compound Poisson distributions. Explicit formulas for the mean and variance that are highly accurate are given. For random clocked loads, a stochastic bound is provided for the discrepancy between the exact and approximate distributions. For deterministic clocked loads, sample path bounds are found. Simulation results are given to demonstrate the accuracy of the model     

Overload control in finite-buffer multiclass message systems

A finite-capacity message system which handles several traffic types with different priority classes is considered. An overload control scheme is proposed which aims to maintain a strategic reserve of buffers for the higher priority traffic classes. Associated with each traffic class are two thresholds: ablocking threshold and aresume threshold. At the epoch when the buffer occupancy level reaches a blocking threshold, the priority class associated with that threshold is blocked. Similarly, at the epoch when the buffer occupancy level decreases to a resume threshold, the admission of the priority class associated with that threshold is resumed. The scheme is analyzed by means of the Green's function method, and closed-form results are obtained for the mean delay of admitted messages, the blocking probability for each priority class, and the ergodic state probabilities.