This paper presents an analytical approximate and computationally tractable technique for the transient analysis of finite capacity Markovian networks. The approach is based on a network decomposition that is unique, it decomposes the network into overlapping (non-disjoint) subnetworks. The model approximates the transient queue-length distributions of the subnetworks. It is computationally tra...

This paper refers to some closed two-stage queueing systems with state-dcpendent vacation policy. By means of the markovian rcnewal process and the stochastic decomposition formulas of the quantities in equilibrium for M/Gjl vacation models, we derive both stationary distributions of the queue length and the cyclic time for the closed state-dependcnt vacation model. We try to so!\'e the problem...

In this paper a study on the buffer overflow period in a finite-buffer queue is presented. A special attention is paid to the autocorrelation and batch arrivals, which are supposed to mimic the properties of real arrival processes. Using the batch Markovian arrival process, formulas for the duration of the first, subsequent and stationary overflow periods, as well as formulas for the distributi...

This paper provides an analytical model for the performance evaluation of a two class DiffServ link. It is applicable for the performance analysis of Data traffic in the presence of higher priority Constant Bit Rate (CBR) encoded Voice and Video traffic. The DiffServ link is modeled as a single server queue in a Markovian environment. The queueing performance of data packets is evaluated by mat...

In this paper we introduce and analyze a model of a multiplexer queue with a batch Markovian arrival process and a special, timer based, non-work-conserving service discipline. We show that the embedded process at departures is an M/G/1 type process with proper state partitioning, which can be efficiently analyzed by matrix geometric methods. We derive the expressions to compute the distributio...

In this paper, we present a performance analysis of a 2-dimensional preemptive priority queueing system with state-dependent arrivals. Using a Markovian formulation we first compute the steady state distribution for the queue length of both classes. Then, waiting times and busy periods are characterized through (i) first and second moments and (ii) the approximation of their cumulative distribu...

We consider ordinary and conditional first passage times in a general birth–death process. Under existence conditions, we derive closed-form expressions for the kth order moment of the defined random variables, k ≥ 1. We also give an explicit condition for a birth–death process to be ergodic degree 3. Based on the obtained results, we analyze some applications for Markovian queueing systems. In...

This paper analyzes large deviation probabilities related to the number of customers in a Markov modulated infinite-server queue, with state-dependent arrival and service rates. Two specific scalings are studied: in the first, just the arrival rates are linearly scaled by N (for large N ), whereas in the second in addition the Markovian background process is sped up by a factor N , for some > 0...

Transient analysis of non-Markovian Stochastic Petri nets is a theoretically interesting and practically important problem. We present a new method to compute bounds and an approximation on the average state sojourn times for a special class of deterministic and stochastic Petri nets (DSPNs). In addition to the idea of the subordinated Markov chain traditionally used for the stationary solution...

This paper analyzes a single-server finite-buffer vacation (single and multiple) queue wherein the input process follows a discrete-time batch Markovian arrival process (D-BMAP). The service and vacation times are generally distributed and their durations are integral multiples of a slot duration. We obtain the state probabilities at service completion, vacation termination, arbitrary, and prea...