A queueing process with the possibility of customers becoming servers

1991 ◽  
Vol 23 (4) ◽  
pp. 957-971
Author(s):  
Wen-Jang Huang ◽  
Prem S. Puri
Keyword(s):  
Asymptotic Behavior ◽  
Joint Distribution ◽  
Queueing System ◽  
Waiting Times ◽  
Queueing Systems ◽  
Queue Size ◽  
Queueing Process

A new queueing system called G/G/{p} is introduced and studied. In this queue, unlike standard queues, the customers after being served are allowed to become servers themselves. More precisely, at the completion of his service each customer is assumed to become a server with probability p or leave the system with probability 1 – p, independent of everything else. We make some comparisons about the waiting times and queue sizes among different queueing systems. We also study the joint distribution of the queue size, the number of servers and the number of departures at time t for exact and asymptotic behavior for large t.

A queueing process with the possibility of customers becoming servers

1991 ◽  
Vol 23 (04) ◽  
pp. 957-971
Author(s):  
Wen-Jang Huang ◽  
Prem S. Puri
Keyword(s):  
Asymptotic Behavior ◽  
Joint Distribution ◽  
Queueing System ◽  
Waiting Times ◽  
Queueing Systems ◽  
Queue Size ◽  
Queueing Process

A new queueing system called G/G/{p} is introduced and studied. In this queue, unlike standard queues, the customers after being served are allowed to become servers themselves. More precisely, at the completion of his service each customer is assumed to become a server with probability p or leave the system with probability 1 – p, independent of everything else. We make some comparisons about the waiting times and queue sizes among different queueing systems. We also study the joint distribution of the queue size, the number of servers and the number of departures at time t for exact and asymptotic behavior for large t.

The GI/G/1 queue with uniformly limited virtual waiting times; the finite dam

1980 ◽  
Vol 12 (2) ◽  
pp. 501-516 ◽  
Author(s):  
Do Le Minh
Keyword(s):  
Water Supply ◽  
Analytical Method ◽  
Busy Period ◽  
Queueing System ◽  
Waiting Times ◽  
Fixed Interval ◽  
Finite Capacity ◽  
Queueing Process ◽  
Finite Dam

This paper studies the GI/G/1 queueing system in which no customer can stay longer than a fixed interval D. This is also a model for the dam with finite capacity, instantaneous water supply and constant release rule. Using analytical method together with the property that the queueing process ‘starts anew’ probabilistically whenever an arriving customer initiates a busy period, we obtain various transient and stationary results for the system.

A solvable model for a finite-capacity queueing system

1985 ◽  
Vol 22 (4) ◽  
pp. 903-911 ◽  
Author(s):  
V. Giorno ◽  
C. Negri ◽  
A. G. Nobile
Keyword(s):  
Queueing System ◽  
Waiting Times ◽  
Queueing Systems ◽  
Solvable Model ◽  
Probability Density Functions ◽  
Single Server ◽  
Finite Capacity ◽  
System Service ◽  
Transient Probabilities ◽  
Number Of Customers

Single–server–single-queue–FIFO-discipline queueing systems are considered in which at most a finite number of customers N can be present in the system. Service and arrival rates are taken to be dependent upon that state of the system. Interarrival intervals, service intervals, waiting times and busy periods are studied, and the results obtained are used to investigate the features of a special queueing model characterized by parameters (λ (Ν –n), μn). This model retains the qualitative features of the C-model proposed by Conolly [2] and Chan and Conolly [1]. However, quite unlike the latter, it also leads to closed-form expressions for the transient probabilities, the interarrival and service probability density functions and their moments, as well as the effective interarrival and service densities and their moments. Finally, some computational results are given to compare the model discussed in this paper with the C-model.

The GI/G/1 queue with uniformly limited virtual waiting times; the finite dam

1980 ◽  
Vol 12 (02) ◽  
pp. 501-516 ◽  
Author(s):  
Do Le Minh
Keyword(s):  
Water Supply ◽  
Analytical Method ◽  
Busy Period ◽  
Queueing System ◽  
Waiting Times ◽  
Fixed Interval ◽  
Finite Capacity ◽  
Queueing Process ◽  
Finite Dam

This paper studies the GI/G/1 queueing system in which no customer can stay longer than a fixed interval D. This is also a model for the dam with finite capacity, instantaneous water supply and constant release rule. Using analytical method together with the property that the queueing process ‘starts anew’ probabilistically whenever an arriving customer initiates a busy period, we obtain various transient and stationary results for the system.

A solvable model for a finite-capacity queueing system

1985 ◽  
Vol 22 (04) ◽  
pp. 903-911 ◽  
Author(s):  
V. Giorno ◽  
C. Negri ◽  
A. G. Nobile
Keyword(s):  
Queueing System ◽  
Waiting Times ◽  
Queueing Systems ◽  
Solvable Model ◽  
Probability Density Functions ◽  
Single Server ◽  
Finite Capacity ◽  
System Service ◽  
Transient Probabilities ◽  
Number Of Customers

Single–server–single-queue–FIFO-discipline queueing systems are considered in which at most a finite number of customers N can be present in the system. Service and arrival rates are taken to be dependent upon that state of the system. Interarrival intervals, service intervals, waiting times and busy periods are studied, and the results obtained are used to investigate the features of a special queueing model characterized by parameters (λ (Ν –n), μn). This model retains the qualitative features of the C-model proposed by Conolly [2] and Chan and Conolly [1]. However, quite unlike the latter, it also leads to closed-form expressions for the transient probabilities, the interarrival and service probability density functions and their moments, as well as the effective interarrival and service densities and their moments. Finally, some computational results are given to compare the model discussed in this paper with the C-model.

scholarly journals Queueing systems for multiple FBM-based traffic models

2005 ◽  
Vol 46 (3) ◽  
pp. 361-377 ◽  
Author(s):  
Mihaela T. Matache ◽  
Valentin Matache
Keyword(s):  
Brownian Motion ◽  
Upper Bound ◽  
Busy Period ◽  
Queueing System ◽  
Queueing Systems ◽  
Traffic Model ◽  
Queue Size ◽  
Buffer Allocation ◽  
Traffic Models ◽  
Overflow Probability

AbstractA multiple fractional Brownian motion (FBM)-based traffic model is considered. Various lower bounds for the overflow probability of the associated queueing system are obtained. Based on a probabilistic bound for the busy period of an ATM queueing system associated with a multiple FBM-based input traffic, a minimal dynamic buffer allocation function (DBAF) is obtained and a DBAF-allocation algorithm is designed. The purpose is to create an upper bound for the queueing system associated with the traffic. This upper bound, called a DBAF, is a function of time, dynamically bouncing with the traffic. An envelope process associated with the multiple FBM-based traffic model is introduced and used to estimate the queue size of the queueing system associated with that traffic model.

scholarly journals On a first passage problem in general queueing systems with multiple vacations

1992 ◽  
Vol 5 (2) ◽  
pp. 177-192 ◽  
Author(s):  
Jewgeni H. Dshalalow
Keyword(s):  
Preliminary Analysis ◽  
Queueing System ◽  
Queueing Systems ◽  
Compound Poisson Process ◽  
Single Server ◽  
New Techniques ◽  
Queueing Process ◽  
Multiple Vacation ◽  
State Dependent ◽  
First Passage Problem

The author studies a generalized single-server queueing system with bulk arrivals and batch service, where the server takes vacations each time the queue level falls below r(≥1) in accordance with the multiple vacation discipline. The input to the system is assumed to be a compound Poisson process modulated by the system and the service is assumed to be state dependent. One of the essential part in the analysis of the system is the employment of new techniques related to the first excess level processes. A preliminary analysis of such processes and recent results of the author on modulated processes enabled the author to obtain all major characteristics for the queueing process explicitly. Various examples and applications are discussed.

scholarly journals A model for waiting times for non-stationary queueing systems

2016 ◽  
Vol 6 (1) ◽  
pp. 68-71
Author(s):  
Mihir Dash
Keyword(s):  
Stochastic Models ◽  
Queueing System ◽  
Waiting Times ◽  
Queueing Systems ◽  
The Other ◽  
Queueing Models ◽  
Simulation Methods ◽  
Other Hand

Queueing models are stochastic models that represent the probability that a queueing system will be found in a particular configuration or state. Several interesting stationary queueing systems have been solved analytically; on the other hand, non-stationary queueing systems are relatively unexplored. The present study analyses the waiting times of a non-stationary M/M/1 queueing system using simulation methods.

OPTIMIZATION OF MARKOV SYSTEMS OF QUEUEING WITH WAITING TIME IN THE MATLAB SYSTEM

2017 ◽  
pp. 39-47
Author(s):  
Viktor Afonin ◽  
Vladimir Valer'evich Nikulin
Keyword(s):  
Queueing System ◽  
Queueing Systems ◽  
Random Variable ◽  
Model Systems ◽  
Queuing Systems ◽  
Input Flow ◽  
Continuous Random Variable ◽  
Input Stream ◽  
Time Intervals ◽  
Markov Systems

The article focuses on attempt to optimize two well-known Markov systems of queueing: a multichannel queueing system with finite storage, and a multichannel queueing system with limited queue time. In the Markov queuing systems, the intensity of the input stream of requests (requirements, calls, customers, demands) is subject to the Poisson law of the probability distribution of the number of applications in the stream; the intensity of service, as well as the intensity of leaving the application queue is subject to exponential distribution. In a Poisson flow, the time intervals between requirements are subject to the exponential law of a continuous random variable. In the context of Markov queueing systems, there have been obtained significant results, which are expressed in the form of analytical dependencies. These dependencies are used for setting up and numerical solution of the problem stated. The probability of failure in service is taken as a task function; it should be minimized and depends on the intensity of input flow of requests, on the intensity of service, and on the intensity of requests leaving the queue. This, in turn, allows to calculate the maximum relative throughput of a given queuing system. The mentioned algorithm was realized in MATLAB system. The results obtained in the form of descriptive algorithms can be used for testing queueing model systems during peak (unchanged) loads.

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