Priority Queue Discipline Research Articles

A family of delay-dependent dynamic priority queueing systems

We consider a family of single-server queueing systems with two priority classes. The system operates under a dynamic priority queue discipline in which the relative priorities of customers increase with their waiting times, and which can be characterized by the urgency number. We investigate the transient as well as the steady-state behavior of the virtual waiting times of the two classes of customer as functions of the urgency number. Stochastic orderings, the joint distribution, and surprising limit results for these processes are obtained for the first time.

Delay Analysis of a Time Division Multiple Access (TDMA) Channel

The delay performance of a Time Division Multiple Access (TDMA) channel for transmitting data messages is considered. The channel is assumed to be fixed assigned to a station with unlimited buffer capacity and Poisson message arrivals. Each message gives rise to one or more packets for transmission into fixed-length time slots. The steady-state probability generating function of the queue size is derived. A formula for the expected message delay is given. The analysis is then generalized to a nonpreemptive priority queue discipline; expected message delay formulas are given for the priority classes.

Analysis of the Earliest Due Date Scheduling Rule in Queueing Systems

We investigate a model for a general single server queueing system operating under the earliest due date scheduling rule, which can be interpreted more generally as a dynamic priority queue-discipline. We consider both preemptive resume and non preemptive disciplines within this framework. No assumptions are made about the distributions of interarrival times and service times of customers in this model, so that characterizations can be derived for arbitrary systems. The analysis depends on suitably defining the concepts of the server's workload and busy period of the system with respect to the priority classes involved. Equations are developed for the virtual waiting times of customers arriving at the system at any time t, and these imply properties of virtual lateness. In the case of an M/G/1 system, expressions for mean waiting times in transient and steady state are derived, and these are found to be analogous to the expressions derived by Cobham in the special case of static priorities. Bounds for expected waiting lime and lateness are obtained, and the increased flexibility of optimization with respect to dynamic priorities is indicated. The results in the paper extend to the case of a number of servers in parallel instead of a single server.

Weaving Processes-Effects of Non-Preemptive Priority and Operator Interference on Output

Warp yarns are depleted in the weaving process and must be replaced. Principles of queueing theory are applied to warp beam replacement. Looms may be serviced with new warp beams on a first-come-first-served or on a priority basis. Comparative studies have been made to determine the queueing dis cipline that would maximize loom output or loom operating efficiency for the same number of repairmen. Monte Carlo methods have been used for examining the queueing process. The actual universe of looms was replaced by a mathematical model that was demonstrated to be theoretically equivalent to the actual universe. For the particular system investigated, the priority queue discipline proved to be marginally more economical than the first-come-first-served discipline. The effectiveness of simulation as a tool for this type of study has been demonstrated.