Abstract: The target of this research in the queueing theory is to prove the law of the iterated logarithm (LIL) under the conditions of heavy traffic in multiphase queueing systems. In this paper, the LIL for global maxima is proved in the phases of a queueing system studied for an important probability characteristic of the system (total waiting time of a customer and waiting time of a custom...

Moment sequences associated with probability distributions can be sources of integer sequences. Operators on probability distributions correspond to operators on integer sequences. Thus, there is an opportunity to apply each theory to the other. Moreover, probability models can be sources of integer sequences, both classical and new, as we show by considering the classical M/G/1 single-server q...

Many authors have analyzed queueing systems with server breakdowns. Kendall (1953) studied stochastic processes occurring in the theory of queues and their analysis by the method of imbedded Markov chains. Buzacott and Hanifin (1978) classified the machine failures as operation dependent failures and time dependent failures. Shanthikumar (1982) analyzed a M/G/1 queueing system with time and ope...

In this paper, we propose the use of a control theoretical approach in the design of fair queueing algorithms based on the Scalable Core (SCORE) / Dynamic Packet State (DPS) architecture. In particular, we make use of the Linear Quadratic control method from optimal control theory to design stable and robust systems that are simple to implement. Simulation results show that this approach gives ...

Obtaining (tail) probabilities from a transform function is an important topic in queueing theory. To obtain these probabilities in discrete-time queueing systems, we have to invert probability generating functions, since most important distributions in discrete-time queueing systems can be determined in the form of probability generating functions. In this paper, we calculate the tail probabil...

In this paper, we derive worst case bounds on delay and backlog for non-preemptive priority queueing systems using network calculus. There are known results for the average behaviour of non-preemptive priority queueing systems from traditional queueing theory. By use of numerical investigations, we compare our worst case bounds to those average behaviour results in order to give a feel as to ho...

Professor emeritus Lajos Takács passed away on December 4, 2015, in Cleveland Heights, Ohio. He is survived by his wife Dalma, their two daughters Judith and Susan, and their families. Lajos Takács will be remembered as a brilliant mathematician, a groundbreaking contributor to the theory of stochastic processes, a world-leading queueing theorist, and a very kind person. We provide here a short...

We investigate here how to treat numerically the Kendall functional equation occuring in the theory of branching processes and queueing theory. We discuss this question in the context of priority queueing systems with switchover times. In numerical analysis of such systems one deals with functional equations of the Kendall type and efficient numerical treatment of these is necessary in order to...

This paper describes how a combined queueing and simulation study was successfully executed for the design of a toll plaza. The objectives of the study were twofold: • to configure the types of toll booths with multiple payment functionalities (cash, credit cards, and electronic payment). • to determine the number of toll booths for each type. The model was also used to validate the spacing, sa...