A queuing system, is a dynamical system whose state evolves in time by the occurrence of events at possibly irregular time intervals. Placetransitions Petri nets (commonly called Petri nets) are a graphical and mathematical modeling tool applicable to queuing systems in order to represent its states evolution. Timed Petri nets are an extension of Petri nets, where now the timing at which the st...

The paper is devoted on computer simulation of rare event probability, which is a critical issue in areas such as reliabilities, telecommunications, aircraft management, etc. This means that it is necessary to evaluate probabilityties less than 10, which is unreasonable to be simulated with standard Monte Carlo approach. M/M/1/N queuing system and tandem queuing system are under investigation w...

Multi-class closed queuing networks with synchronization stations find applications in analytical models of assembly systems and production systems operating under pull control policies. These queuing networks are hard to analyze exactly and therefore approximation methods must be used for performance evaluation. In this research we propose a new efficient approach based on parametric decomposi...

This paper defines the building blocks of and derives basic queuing systems. It begins with a review of some probability theory and then defines processes used to analyze queuing systems, in particular the birth-death process. A few simple queues are analyzed in terms of steady-state derivation before the paper discusses some attempted field research on the topic.

We present a systematic treatment of efficient nonlinear optimizations of queuing systems. The suite of formulations uses the computational tool of convex optimization, with fast polynomial time algorithms to obtain the global optimum for these nonlinear problems under various constraints. We first show convexity structures of several queuing systems, including some surprising transition patter...

This paper studies a Markov model of queuing-inventory system with primary, retrial, and feedback customers. Primary customers form Poisson flow, if an inventory level is positive upon their arrival, they instantly receive the items. If equal to zero arrival primary customer, then this according Bernoulli scheme, either leaves or goes into infinite buffer repeat request in future. The rate retr...