Mathematical Model For Forwarding Packets In Communication Network

In recent years, SDN technology has been applied to several networks such as wide area network (WAN). IT provides many benefits, such as: enhancing data transfer, promoting Application performance and reducing deployment costs. Software Defined-WAN networks lack studies and references. This paper introduced a system for SD-WAN network using PH/PH/C queues. It concentrates on the study of algebraic estimates the probability distribution of the system states. The Matrix-Geometric solution procedure of a phase type distribution queue with first-come first-served discipline is used.

The analysis of discrete time Geom/Geom/1 queue with single working vacation and multiple vacations (Geom/Geom/1/SWV+MV)

In this article, we consider a discrete-time Geom/Geom/1 queue with two phase vacation policy that comprises single working vacation and multiple vacations, denoted by Geom/Geom/1/SWV+MV. For this model, we first derive the explicit expression for the stationary system size by the matrix-geometric solution method. Next, we obtain the stochastic decomposition structures of system size and the sojourn time of an arbitrary customer in steady state. Moreover, the regular busy period and busy cycle are analyzed by limiting theorem of alternative renewal process. Besides, some special cases are presented and the relationship between the Geom/Geom/1/SWV+MV queue and its continuous time counterpart is investigated. Finally, we perform several experiments to illustrate the effect of model parameters on some performance measures.

On the GI/M/1 Queue with Vacations and Multiple Service Phases

This paper considers a GI/M/1 queue with vacations and multiple service phases. Whenever the system becomes empty, the server takes a vacation, causing the system to move to vacation phase 0. If the server returns from a vacation to find no customer waiting, another vacation begins. Otherwise, the system jumps from phase 0 to some service phase i with probability qi, i=1,2,…,N. Using the matrix geometric solution method and semi-Markov process, we obtain the distributions of the stationary system size at both arrival and arbitrary epochs. The distribution of the stationary waiting time of an arbitrary customer is also derived. In addition, we present some performance measures such as mean waiting time of an arbitrary customer, mean length of the type-i cycle, and mean number of customers in the system at the end of phase 0. Finally, some numerical examples are presented.

Fluid Model Driven by an M/M/1 Queue with Set-Up and Close-Down Period

The fluid model driven by an M/M/1 queue with set-up and close-down period is studied. The Laplace transform of the joint stationary distribution of the fluid model is of matrix geometric structure. With matrix geometric solution method, the Laplace-Stieltjes transformation of the stationary distribution of the buffer content is obtained, as well as the mean buffer content. Finally, with some numerical examples, the effect of the parameters on mean buffer content is presented.

The Geo/Geo/1+1 Queueing System with Negative Customers

We study a Geo/Geo/1+1 queueing system with geometrical arrivals of both positive and negative customers in which killing strategies considered are removal of customers at the head (RCH) and removal of customers at the end (RCE). Using quasi-birth-death (QBD) process and matrix-geometric solution method, we obtain the stationary distribution of the queue length, the average waiting time of a new arrival customer, and the probabilities of servers in busy or idle period, respectively. Finally, we analyze the effect of some related parameters on the system performance measures.

Analysis of the GI/Geo/c Queue with Working Vacations

Working vacation queue models are well applied in the modeling and analysis of the router in optical networks. The GI/Geo/c queue with working vacations is studied in this paper. Through establishing two-dimensional Markov chain and using matrix-geometric solution method, the stability condition is derived. Adopting UL-type RG-factorization of irreducible Markov chain, the stationary distribution is given. Based on these, the probability distribution of queue-length and PGF of waiting time are obtained in the end.