This paper introduces an analytical method for approximating the performability of a firm realtime system modeled by a multi-server queue. The service discipline in the queue is earliestdeadline- first (EDF), which is an optimal scheduling algorithm. Real-time jobs with exponentially distributed relative deadlines arrive according to a Poisson process. All jobs have deadlines until the end of s...

A M/M/1 queue with catastrophes is a modified model for which, according to the times of Poisson process, occur leaving system empty. In this work, we study fractional catastrophes, which formulated by considering derivatives in Kolmogorov’s Forward Equations original Markov process. For resulting obtain state probabilities, mean and variance number customers at any time. addition, discuss esti...

A class of discrete-time priority queueing systems with Markov modulated arrivals is considered. In these systems, N queues are served by a single server according to priorities that are preassigned to the queues. Packet arrivals are modeled as discrete-time batch processes with a distribution that depends on the state of an independent common two-state Markov chain. This allows to cover a wide...

We consider n M/M/1 queues in series. At queue one the arrival and service rates are chosen in pair from a finite set whenever there are arrivals or service completions at any queue. Customers arriving to queue k (k = 1, 2, ..., n − 1) must go on to queue k + 1 after finishing service at server associated queue k. Customers arriving to queue n leave the system after finishing service at the la...

This paper studies the classification problem of discrete time and continuous time Markov processes of matrix M/G/1 type with a tree structure. It is shown that the Perron-Frobenius eigenvalue of a nonnegative matrix provides information for a complete classification of the Markov process of interest. A computational method is developed to find whether a Markov process of matrix M/G/1 type with...

We study a single station two-stage reneging queue with Poisson arrivals, exponential services, and two levels of behaviors, extending the popular Erlang A model that assumes constant rate. derive approximate analytical formulas representing performance measures for our following Markov chain decomposition approach. Our not only give accurate results spanning heavy-traffic to light-traffic regi...

Abstract We propose dual form of Markov renewal equations. While the dual form is theoretically equivalent to the classical standard form of Markov renewal equation, it is shown to be a useful tool for analysis of recent stochastic models. To demonstrate the power of the dual form of Markov renewal equations, we apply one to tail asymptotic analysis of the stationary workload distribution for a...

Recent work on congestion control in TCP/IP networks combines improved end-user transmission mechanisms with active queue management schemes at network routers. An active queue management scheme consists of two stages. In order to stabilize the queues at a router, one must first determine an appropriate packet marking probability given the current degree of congestion. Second, in order to reali...

Motivated by the dispatching of trucks to shovels in surface mines, we study optimal routing in a Markovian finite-source, multi-server queueing system with heterogeneous servers, each with a separate queue. We formulate the problem of routing customers to servers to maximize the system throughput as a Markov Decision Process. When the servers are homogenous, we demonstrate that the Shortest Qu...

This paper analyzes a discrete-time finite-buffer multi-server bulk-service queueing system in which the interarrival-and service-times are, respectively, arbitrarily and geometrically distributed. Using the supplementary variable and the imbedded Markov-chain techniques, the queue is analyzed for the early arrival system. We obtain state probabilities at prearrival, arbitrary and outside obser...