Performance analysis of a discrete-time queueing system with customer deadlines

This paper studies a discrete-time queueing system where each customer has a maximum allowed sojourn time in the system, referred to as the "deadline" of the customer. Deadlines of consecutive customers are modelled as independent and geometrically distributed random variables. The arrival process of new customers, furthermore, is assumed to be general and independent, while service times of the customers are deterministically equal to one slot each. For this queueing model, we are able to obtain exact formulas for quantities as the mean system content, the mean customer delay, and the deadline-expiration ratio. These formulas, however, contain infinite sums and infinite products, which implies that truncations are required to actually compute numerical values. Therefore, we also derive some easy-to-evaluate approximate results for the main performance measures. These approximate results are quite accurate, as we show in some numerical examples. Possible applications of this type of queueing model are numerous: the (variable) deadlines could model, for instance, the fact that customers may become impatient and leave the queue unserved if they have to wait too long in line, but they could also reflect the fact that the service of a customer is not useful anymore if it cannot be delivered soon enough, etc

Performance comparison of several priority schemes with priority jumps

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Controlling delay differentiation with priority jumps: analytical study

Supporting different services with different Quality of Service (QoS) requirements is not an easy task in modern telecommunication systems: an efficient priority scheduling discipline is of great importance. Fixed or static priority achieves maximal delay differentiation between different types of traffic, but may have a too severe impact on the performance of lower-priority traffic. In this paper, we propose a priority scheduling discipline with priority jumps to control the delay differentiation. In this scheduling discipline, packets can be promoted to a higher priority level in the course of time. We use probability generating functions to study the queueing system analytically. Some interesting mathematical challenges thereby arise. With some numerical examples, we finally show the impact of the priority jumps and of the system parameters