In discrete event simulation, very often the future event set is represented by a priority queue. The data structure used to implement the queue and the way operations are performed on it are often crucial to the execution time of a simulation. In this paper a new priority queue implementation strategy, the Lazy Queue, is presented. It is tailored to handle operations on the pending event set e...

In this paper, we study the performance of service systems with priority upgrades. We model the service system as a single-server two-class priority queue, with queue 1 as the normal queue and queue 2 as the priority queue. The queueing model of interest has various applications in healthcare services, perishable inventory and project management. We comprehensively examine the system’s stationa...

Two random traffic streams are competing for the service time of a single server (multiplexer). The streams form two queues, primary (queue 1) and secondary (queue 0). The primary queue is served exhaustively, after which the server switches over to queue 0. The duration of time the server resides in the secondary queue is determined by the dynamic evolution in queue 1. If there is an arrival t...

We prove that the Besicovitch Covering Property (BCP) does not hold for some classes of homogeneous quasi-distances on Carnot groups of step 3 and higher. As a special case we get that, in Carnot groups of step 3 and higher, BCP is not satisfied for those homogeneous distances whose unit ball centered at the origin coincides with a Euclidean ball centered at the origin. This result comes in con...

Increasing availability of high-speed Internet and wireless access points has allowed home users to connect not only their computers but various other devices to the Internet. Every device running different applications requires unique Quality of Service (QoS). It has been shown that delay-sensitive applications, such as VoIP, remote login and online game sessions, suffer increased latency in t...

This paper presents a novel technique to derive asymptotic expressions for rare event probabilities for random walks in the quarter plane. For concreteness, we study a tandem queue with Poisson arrivals, exponential service times and coupled processors. The service rate for one queue is only a fraction of the global service rate when the other queue is non empty; when one queue is empty, the ot...