This paper examines a discrete-time queuing system with applications to telecommunications traffic. The arrival process is a particular Markov modulated process which belongs to the class of discrete batched Markovian arrival processes. The server process is a single server deterministic queue. A closed form exact solution is given for the expected queue length and delay. A simple system of equ...

In this paper, we discuss the waiting-time distribution for a finite-space, single-server queueing system, in which customers arrive singly following Poisson process and server operates under (a,b)-bulk service rule. The system has finite-buffer capacity ‘N’ excluding batch service. service-time of batches follows general distribution, is independent arrival process. We first develop an alterna...

Delay or queue length information has the potential to influence the decision of a customer to use a service system. Thus, it is imperative for service system managers to understand how the information that they provide will affect the performance of the system. To this end, we construct and analyze two two-dimensional deterministic fluid models that incorporate customer choice behavior based o...

In this paper, we propose a method for finding the optimum information queue length of a palmtop multimedia terminal. which is equipped with semi-batch power management. This optimum queue length is determined by the minimization of power consumption, which is based on the balance of the probability combination of high-power state and low-power state. The low-power states are derived from the “...

This paper presents a discrete-time single-server finite buffer N threshold policy queue with renewal input and discrete Markovian service process. The server terminates service whenever the system becomes empty, and recommences service as soon as the number of waiting customers in the queue is N . We obtain the system-length distributions at prearrival and arbitrary epochs using the supplement...

Formulas relating the mean queue length, utilization, and coefficient of variation of service time of a queue during a given observation period are derived using operational analysis. The main formula, a counterpart of the Pollaczek-Khintchin formula for M/G/l queues, relies on four homogeneity assumptions. The other formulas require fewer assumptions. Simulation experiments compare the robustn...

This article considers Gaussian flows which are fed into a GPS (Generalized Processor Sharing) scheduler. The system is analyzed using a most probable path approach. This method gives quite good approximations for performance measures, like queue length distributions in the full range of queue levels. The approximations are based on the distinction whether it is more probable that an aggregated...

This paper presents a novel methodology for approximating the queue length (the number of customers in the system) distributions of time-varying non-Markovian manyserver queues (e.g., Gt/Gt/nt queues), where the number of servers (nt) is large. Our methodology consists of two steps. The first step uses phase-type distributions to approximate the general inter-arrival and service times, thus gen...

The Active Queue Management algorithms stabilize the instantaneous queue length through mapping the congestion measurement into packet drop probability to achieve high throughput and low average delay. Random Early Detection [RED] is widely used AQM mechanism detecting and avoiding the incipient congestion. The detection of congestion is based on priori estimation of congestion and calculation ...

We develop approximate solutions for the equilibrium queue length probability distribution of queues in open Markovian networks by considering each queue independently, constructing its arrival process as the join of each contributing queue's departing traffic. Without modulation and non-unit batches, we would only need to consider mean internal traffic rates, modelling each queue as M/M/1 to g...