On congestion systems with negative exponential desired service time distributions

1966 ◽  
Vol 18 (1) ◽  
pp. 223-228 ◽  
Author(s):  
D. N. Shanbhag
Keyword(s):  
Service Time ◽  
Negative Exponential

An approximation for the busy period of the M/G/1 queue using a diffusion model

1974 ◽  
Vol 11 (1) ◽  
pp. 159-169 ◽  
Author(s):  
D. P. Heyman
Keyword(s):  
Density Function ◽  
Diffusion Model ◽  
Gamma Distribution ◽  
Service Time ◽  
Busy Period ◽  
Exact Density ◽  
Mean And Variance ◽  
Negative Exponential

A diffusion model for the M/G/1 queue due to D. P. Gaver is used to obtain an approximation for the density function of the busy period. The approximation has the same mean and variance as the exact density function, and can be given explicitly when the service time is constant, or has a negative exponential or gamma distribution, or is a mixture of these types.

Networks of queues with customers of different types

1975 ◽  
Vol 12 (3) ◽  
pp. 542-554 ◽  
Author(s):  
F. P. Kelly
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Service Time Distribution ◽  
Basic Model ◽  
Open Case ◽  
Negative Exponential Distribution ◽  
Different Types ◽  
The Individual ◽  
Negative Exponential ◽  
Networks Of Queues

The behaviour in equilibrium of networks of queues in which customers may be of different types is studied. The type of a customer is allowed to influence his choice of path through the network and, under certain conditions, his service time distribution at each queue. The model assumed will usually cause each service time distribution to be of a form related to the negative exponential distribution.Theorems 1 and 2 establish the equilibrium distribution for the basic model in the closed and open cases; in the open case the individual queues are independent in equilibrium. In Section 4 similar results are obtained for other models, models which include processes better described as networks of colonies or as networks of stacks. In Section 5 the effect of time reversal upon certain processes is used to obtain further information about the equilibrium behaviour of those processes.

A correlated queue with infinitely many servers

1986 ◽  
Vol 23 (01) ◽  
pp. 155-165 ◽  
Author(s):  
C. Langaris
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Service Time ◽  
Transient State ◽  
Laplace Transforms ◽  
Bivariate Distribution ◽  
Numerical Calculations ◽  
Output Process ◽  
Negative Exponential ◽  
Steady State Probabilities

This work analyses a queueing mechanism with infinitely many servers in which the interarrival interval T preceding the arrival of a customer and his service time S are assumed correlated. A bivariate distribution with negative exponential marginals is used and the Laplace transforms pn (z) of the system probabilities in transient state are obtained. Closed-form expressions for the steady-state probabilities pn and their moments are given too. Finally the output process is investigated and conclusions are drawn from numerical calculations.

A correlated queue with infinitely many servers

1986 ◽  
Vol 23 (1) ◽  
pp. 155-165 ◽  
Author(s):  
C. Langaris
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Service Time ◽  
Transient State ◽  
Laplace Transforms ◽  
Bivariate Distribution ◽  
Numerical Calculations ◽  
Output Process ◽  
Negative Exponential ◽  
Steady State Probabilities

This work analyses a queueing mechanism with infinitely many servers in which the interarrival interval T preceding the arrival of a customer and his service time S are assumed correlated. A bivariate distribution with negative exponential marginals is used and the Laplace transforms pn (z) of the system probabilities in transient state are obtained. Closed-form expressions for the steady-state probabilities pn and their moments are given too. Finally the output process is investigated and conclusions are drawn from numerical calculations.

An approximation for the busy period of the M/G/1 queue using a diffusion model

1974 ◽  
Vol 11 (01) ◽  
pp. 159-169 ◽  
Author(s):  
D. P. Heyman
Keyword(s):  
Density Function ◽  
Diffusion Model ◽  
Gamma Distribution ◽  
Service Time ◽  
Busy Period ◽  
Exact Density ◽  
Mean And Variance ◽  
Negative Exponential

A diffusion model for the M/G/1 queue due to D. P. Gaver is used to obtain an approximation for the density function of the busy period. The approximation has the same mean and variance as the exact density function, and can be given explicitly when the service time is constant, or has a negative exponential or gamma distribution, or is a mixture of these types.

scholarly journals A Queueing system with general moving average input and negative exponential service time

1966 ◽  
Vol 6 (2) ◽  
pp. 223-236 ◽  
Author(s):  
C. Pearce
Keyword(s):  
Service Time ◽  
Queueing System ◽  
Moving Average ◽  
Recent History ◽  
History Of ◽  
Negative Exponential

If we think of the input to a queueing system as arising from some process and depending on the history of that process, we might well expect the duration of inter-arrival intervals to depend mostly on the recent history and to a much smaller extent on that which is more remote.

scholarly journals Imbedded Markov chain analysis of single server bulk queues

1964 ◽  
Vol 4 (2) ◽  
pp. 244-263 ◽  
Author(s):  
U. Narayan Bhat
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Queueing Systems ◽  
Arrival Time Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Chain Analysis ◽  
Special Cases ◽  
Poisson Arrivals ◽  
Negative Exponential

SummaryIn this paper results from Fluctuation Theory are used to analyse the imbedded Markov chains of two single server bulk-queueing systems, (i)with Poisson arrivals and arbitrary service time distribution and (ii) with arbitrary inter-arrival time distribution and negative exponential service time. The discrete time transition probailities and the equilibrium behaviour of the queue lengths of the systems have been obtained along with distributions concerning the busy periods. From the general results several special cases have been derived.

Networks of queues with customers of different types

1975 ◽  
Vol 12 (03) ◽  
pp. 542-554 ◽  
Author(s):  
F. P. Kelly
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Service Time Distribution ◽  
Basic Model ◽  
Open Case ◽  
Negative Exponential Distribution ◽  
Different Types ◽  
The Individual ◽  
Negative Exponential ◽  
Networks Of Queues

The behaviour in equilibrium of networks of queues in which customers may be of different types is studied. The type of a customer is allowed to influence his choice of path through the network and, under certain conditions, his service time distribution at each queue. The model assumed will usually cause each service time distribution to be of a form related to the negative exponential distribution. Theorems 1 and 2 establish the equilibrium distribution for the basic model in the closed and open cases; in the open case the individual queues are independent in equilibrium. In Section 4 similar results are obtained for other models, models which include processes better described as networks of colonies or as networks of stacks. In Section 5 the effect of time reversal upon certain processes is used to obtain further information about the equilibrium behaviour of those processes.

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

2018 ◽  
pp. 439
Author(s):  
Hazim Mansour Gorgees ◽  
Bushra Abdualrasool Ali ◽  
Raghad Ibrahim Kathum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Reliability Function ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Technique ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Better Than

     In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

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