System analysis is often needed with respect to both qualitative and quantitative aspects. In the last decades, several formalisms have been developed that attempt to combine these aspects in one description. Present emphasis is on Stochastic Petri Nets. Amongst others, one disadvantage of these formalisms lies with the diiculties when describing scheduling strategies with Petri Net elements. T...

Queuing theory is the study of queues for managing process and objects. In this paper we analyze various models of the Single server queuing system with.Single-sever service node consists of a server plus its queue. If only one service technician, the machine shop model from section 1. 1 is a single-server queue.Queueing theory is the mathematical study of waiting lines, or queues. The MM1 queu...

Abstract—It is known that in many queueing systems fluid limits are deterministic functions. Models and conditions which lead to random fluid limits have not received much attention. This paper is devoted to a study of a queueing network whose fluid limits admit a random and uncountable branching at certain points. Stability conditions for this model are investigated by the use of recent result...

This paper presents a Timed Coloured Petri Nets based programming tool that supports modeling and performance analysis of distributed World Wide Web environments. A distributed Internet system model, initially described in compliance with Queueing Theory (QT) rules, is mapped onto the Timed Coloured Petri Net (TCPN) structure by means of queueing system templates. Then, it is executed and analy...

We have introduced excluded volume effect, which is an important factor to model a realistic pedestrian queue, into queueing theory. The probability distributions of pedestrian number and pedestrian waiting time in a queue have been calculated exactly. Due to time needed to close up the queue, the mean number of pedestrians increases as pedestrian arrival probability (λ) and leaving probability...

Modeling the traffic flow at signalized intersections has been discussed in many works [1][2][3][4]. Though streets and intersections and designed to be Ergodic, the traffic flow during busy hours is not necessarily Ergodic. In this paper, we modeled the traffic at intersection during busy hours by using M/G/1 model. And based on the collected data, we modeled a special service distribution pat...

Keywords: Queueing Tandem queueing system Marked Markovian arrival process Phase-type distribution Laplace–Stieltjes transform a b s t r a c t A tandem queueing system with infinite and finite intermediate buffers, heterogeneous customers and generalized phase-type service time distribution at the second stage is investigated. The first stage of the tandem has a finite number of servers without...

Queueing Systems with Customer Abandonments and Retrials by Song Deng Doctor of Philosophy in Engineering Industrial Engineering & Operations Research University of California, Berkeley Assistant Professor Ying-Ju Chen , Co-chair Professor Zuo-Jun “Max” Shen , Co-chair In queueing theory, the phenomenon that customers get impatient and renege from the system when the waiting time exceeds their ...

Recently results have shown that a single server queue Poisson Pareto Burst Process input has a tail which is bounded by hyperbolic functions. We show that the hyperbolic upper and lower bounds for this system can be very misleading, that this hyperbolic tail result is relevant only from a certain threshold onwards, and the magnitude of this threshold may be very large. We also show that any hy...

Queueing theory is concerned with developing and investigating mathematical models of systems where customers wait for service. The terms customers and servers are generic. Customers could, for example, be humans waiting in a physical line or waiting on hold on the telephone, jobs waiting to be processed in a factory, or tasks waiting for processing in a computer or communication system. Exampl...