scholarly journals Poisson traffic flow in a general feedback queue

2002 ◽  
Vol 39 (03) ◽  
pp. 630-636 ◽  
Author(s):  
Erol A. Peköz ◽  
Nitindra Joglekar
Keyword(s):  
Arrival Process ◽  
Finite Buffer ◽  
Feedback Delay ◽  
Highway Traffic ◽  
Customer Feedback ◽  
Mild Conditions ◽  
Continuous Density ◽  
Poisson Arrivals ◽  
Finite Buffer Queue ◽  
Feedback Queue

Consider a ·/G/kfinite-buffer queue with a stationary ergodic arrival process and delayed customer feedback, where customers after service may repeatedly return to the back of the queue after an independent general feedback delay whose distribution has a continuous density function. We use coupling methods to show that, under some mild conditions, the feedback flow of customers returning to the back of the queue converges to a Poisson process as the feedback delay distribution is scaled up. This allows for easy waiting-time approximations in the setting of Poisson arrivals, and also gives a new coupling proof of a classic highway traffic result of Breiman (1963). We also consider the case of nonindependent feedback delays.

scholarly journals Poisson traffic flow in a general feedback queue

2002 ◽  
Vol 39 (3) ◽  
pp. 630-636 ◽  
Author(s):  
Erol A. Peköz ◽  
Nitindra Joglekar
Keyword(s):  
Arrival Process ◽  
Finite Buffer ◽  
Feedback Delay ◽  
Highway Traffic ◽  
Customer Feedback ◽  
Mild Conditions ◽  
Continuous Density ◽  
Poisson Arrivals ◽  
Finite Buffer Queue ◽  
Feedback Queue

Consider a ·/G/k finite-buffer queue with a stationary ergodic arrival process and delayed customer feedback, where customers after service may repeatedly return to the back of the queue after an independent general feedback delay whose distribution has a continuous density function. We use coupling methods to show that, under some mild conditions, the feedback flow of customers returning to the back of the queue converges to a Poisson process as the feedback delay distribution is scaled up. This allows for easy waiting-time approximations in the setting of Poisson arrivals, and also gives a new coupling proof of a classic highway traffic result of Breiman (1963). We also consider the case of nonindependent feedback delays.

scholarly journals Transient and Stationary Losses in a Finite-Buffer Queue with Batch Arrivals

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Andrzej Chydzinski ◽  
Blazej Adamczyk
Keyword(s):  
Batch Size ◽  
Buffer Size ◽  
Arrival Process ◽  
Time Interval ◽  
Finite Buffer ◽  
Finite Time Interval ◽  
Batch Arrivals ◽  
Batch Markovian Arrival Process ◽  
Buffer Overflows ◽  
Finite Buffer Queue

We present an analysis of the number of losses, caused by the buffer overflows, in a finite-buffer queue with batch arrivals and autocorrelated interarrival times. Using the batch Markovian arrival process, the formulas for the average number of losses in a finite time interval and the stationary loss ratio are shown. In addition, several numerical examples are presented, including illustrations of the dependence of the number of losses on the average batch size, buffer size, system load, autocorrelation structure, and time.

ADMISSION CONTROL WITH INCOMPLETE INFORMATION TO A FINITE BUFFER QUEUE

2006 ◽  
Vol 21 (1) ◽  
pp. 19-46 ◽  
Author(s):  
Dorothée Honhon ◽  
Sridhar Seshadri
Keyword(s):  
Admission Control ◽  
Partial Information ◽  
Control Policy ◽  
Arrival Process ◽  
Finite Buffer ◽  
Optimal Cost ◽  
State Aggregation ◽  
The Cost ◽  
Finite Buffer Queue

We consider the problem of admission control to a multiserver finite buffer queue under partial information. The controller cannot see the queue but is informed immediately if an admitted customer is lost due to buffer overflow. Turning away (i.e., blocking) customers is costly and so is losing an admitted customer. The latter cost is greater than that of blocking. The controller's objective is to minimize the average cost of blocking and rejection per incoming customer. Lin and Ross [11] studied this problem for multiserver loss systems. We extend their work by allowing a finite buffer and the arrival process to be of the renewal type. We propose a control policy based on a novel state aggregation approach that exploits the regenerative structure of the system, performs well, and gives a lower bound on the optimal cost. The control policy is inspired by a simulation technique that reduces the variance of the estimators by not simulating the customer service process. Numerical experiments show that our bound varies with the load offered to the system and is typically within 1% and 10% of the optimal cost. Also, our bound is tight in the important case when the cost of blocking is low compared to the cost of rejection and the load offered to the system is high. The quality of the bound degrades with the degree of state aggregation, but the computational effort is comparatively small. Moreover, the control policies that we obtain perform better compared to a heuristic suggested by Lin and Ross. The state aggregation technique developed in this article can be used more generally to solve problems in which the objective is to control the time to the end of a cycle and the quality of the information available to the controller degrades with the length of the cycle.

Burst ratio in the finite-buffer queue with batch Poisson arrivals

2018 ◽  
Vol 330 ◽  
pp. 225-238 ◽  
Author(s):  
Andrzej Chydzinski ◽  
Dominik Samociuk ◽  
Blazej Adamczyk
Keyword(s):  
Finite Buffer ◽  
Poisson Arrivals ◽  
Finite Buffer Queue

A multiclass feedback queue in heavy traffic

1988 ◽  
Vol 20 (01) ◽  
pp. 179-207 ◽  
Author(s):  
Martin I. Reiman
Keyword(s):  
Random Number ◽  
Queueing System ◽  
Heavy Traffic ◽  
Arrival Process ◽  
Service Discipline ◽  
Reflected Brownian Motion ◽  
One Dimensional ◽  
Heavy Traffic Limit ◽  
Single Station ◽  
Feedback Queue

We consider a single station queueing system with several customer classes. Each customer class has its own arrival process. The total service requirement of each customer is divided into a (possibly) random number of service quanta, where the distribution of each quantum may depend on the customer's class and the other quanta of that customer. The service discipline is round-robin, with random quanta. We prove a heavy traffic limit theorem for the above system which states that as the traffic intensity approaches unity, properly normalized sequences of queue length and sojourn time processes converge weakly to one-dimensional reflected Brownian motion.

A stationary Poisson departure process from a minimally delayed infinite server queue with non-stationary Poisson arrivals

1997 ◽  
Vol 34 (3) ◽  
pp. 767-772 ◽  
Author(s):  
John A. Barnes ◽  
Richard Meili
Keyword(s):  
Queueing System ◽  
Mean Shift ◽  
Intensity Function ◽  
Arrival Process ◽  
Service Time Distribution ◽  
Departure Process ◽  
Periodic Intensity ◽  
Server Queue ◽  
Poisson Arrivals ◽  
The Mean

The points of a non-stationary Poisson process with periodic intensity are independently shifted forward in time in such a way that the transformed process is stationary Poisson. The mean shift is shown to be minimal. The approach used is to consider an Mt/Gt/∞ queueing system where the arrival process is a non-stationary Poisson with periodic intensity function. A minimal service time distribution is constructed that yields a stationary Poisson departure process.

scholarly journals Aspects of Impatience in a Finite Buffer Queue

2012 ◽  
Vol 46 (3) ◽  
pp. 189-209
Author(s):  
Medhi Pallabi ◽  
Amit Choudhury
Keyword(s):  
Finite Buffer ◽  
Finite Buffer Queue
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