It has been shown by many authors that distribution properties of some characteristics in queues are inherited from those of the service times. For instances, Keilson (1978) showed that the length of a busy period in an M/G/l queue has a completely monotone density if so does the service time, Shanthikumar(1988) proved that the waiting time distribution in a GI/G/l queue is DFR if so is the ser...

In this paper, we propose an algorithm to calculate the higher moments of the busy period length of a discretetime M/G/1 type queue with finite buffer. The queueing model has a level-dependent transition probability matrix. Our algorithm is given as a set of recursive formulas which are derived from the relationship among the generating function matrices of the fundamental period. As an example...

Abstract: We study the Nash equilibrium behavior of customers in a discrete-time single-server queue under multiple vacation policy or single vacation policy. Every arriving customer either joins the queue or balks based on his or her service utility. Using a Quasi-Birth-Death Processes (QBD) model, we obtain the stationary distribution of the queue length via the Matrix-Geometric Solution meth...

We not only present an alternative and simpler approach to find steady-state distributions of the number jobs for finite-space queueing model Geo/Ga,Y/1/N using roots inherent characteristic equation, but also correct errors in some published papers. The server has a random service capacity Y, it processes when system is at least ‘a’, threshold value. main advantage this process that gives unif...

In the Operations Research queue-joining literature, beginning with Naor (1969), the queue joining probability is monotonic decreasing in the queue length; the longer the queue, the fewer consumers join. Recent academic and empirical evidence indicates that queue-joining probabilities may not always be decreasing in the queue length. We provide a simple explanation for these non-monotonic queue...

We consider a fluid queue in discrete time with random service rate. Such a queue has been used in several recent studies on wireless networks where the packets can be arbitrarily fragmented. We provide conditions on finiteness of moments of stationary delay, its Laplace-Stieltjes transform and various approximations under heavy traffic. Results are extended to the case where the wireless link ...

This paper presents a model for a discrete time single server G-queue with two types of independent arrivals, namely positive and negative. The arrival of negative customer to queueing system removes one customer from the head of the queue (RCH), which causes server breakdown. The repair of the server is noninstantaneous and after repair server is assumed as good as new. The interarrival times ...

This paper provides steady state queue-size distribution for a G/G/1 queue by using principle of maximum entropy. For this purpose we have used average queue length and normalizing condition as constraints to derive queue-size distribution. Our results give good approximation as demonstrated by taking a numerical illustration. In particular case when square coefficient of variation of inter-arr...

On the basis of establishing mathematical model and defining the parameters and treating embedded Markov chains and probability generating function as math tools, the paper analyzed discrete-time, nonsymmetric dual-threshold service queue system precisely, and it derived first order and second order characteristics of the system. The paper calculates the average queue length and average waiting...

We use a discrete-time dynamical feedback system model of TCP/RED to study the performance of Random Early Detection RED for different values of control parameters. Our analysis shows that the queue length is able to keep stable at a given target if the maximum probability pmax and exponential averaging weight w satisfy some conditions. From the mathematical analysis, a new self-tuning RED is p...