On the waiting time distribution in a generalized queueing system with uniformly bounded sojourn times

1972 ◽  
Vol 9 (03) ◽  
pp. 642-649
Author(s):  
Jacqueline Loris-Teghem
Keyword(s):  
Generating Function ◽  
Waiting Time ◽  
Service Time ◽  
Time Distribution ◽  
Queueing System ◽  
Waiting Time Distribution ◽  
Stieltjes Transform ◽  
Sojourn Times ◽  
Stieltjes Transforms ◽  
Uniformly Bounded

A generalized queueing system with (N+ 2) types of triplets (delay, service time, probability of joining the queue) and with uniformly bounded sojourn times is considered. An expression for the generating function of the Laplace-Stieltjes transforms of the waiting time distributions is derived analytically, in a case where some of the random variables defining the model have a rational Laplace-Stieltjes transform.The standardKl/Km/1 queueing system with uniformly bounded sojourn times is considered in particular.

On the waiting time distribution in a generalized queueing system with uniformly bounded sojourn times

1972 ◽  
Vol 9 (3) ◽  
pp. 642-649 ◽  
Author(s):  
Jacqueline Loris-Teghem
Keyword(s):  
Generating Function ◽  
Waiting Time ◽  
Service Time ◽  
Time Distribution ◽  
Queueing System ◽  
Waiting Time Distribution ◽  
Stieltjes Transform ◽  
Sojourn Times ◽  
Stieltjes Transforms ◽  
Uniformly Bounded

A generalized queueing system with (N + 2) types of triplets (delay, service time, probability of joining the queue) and with uniformly bounded sojourn times is considered. An expression for the generating function of the Laplace-Stieltjes transforms of the waiting time distributions is derived analytically, in a case where some of the random variables defining the model have a rational Laplace-Stieltjes transform.The standard Kl/Km/1 queueing system with uniformly bounded sojourn times is considered in particular.

On the service time distribution and the waiting time process of a potentially infinite capacity queueing system

1969 ◽  
Vol 6 (3) ◽  
pp. 594-603 ◽  
Author(s):  
Nasser Hadidi
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Time Distribution ◽  
Queueing System ◽  
Service Time Distribution ◽  
Waiting Time Distribution ◽  
Poisson Stream ◽  
Waiting Time Process ◽  
The Subject ◽  
Effective Service

In [1] the authors dealt with a particular queueing system in which arrivals occurred in a Poisson stream and the probability differential of a service completion was μσn when the queue contained n customers. Much of the theory could not be carried out further analytically for a general σn, which is a purely n-dependent quantity. To carry the analysis further to the extent of finding the “effective” service time and the waiting time distribution when σn is a linear function of n, (which is considered to be rather general and sufficient for practical purposes), constitutes the subject matter of this paper.

On the service time distribution and the waiting time process of a potentially infinite capacity queueing system

1969 ◽  
Vol 6 (03) ◽  
pp. 594-603 ◽  
Author(s):  
Nasser Hadidi
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Time Distribution ◽  
Queueing System ◽  
Service Time Distribution ◽  
Waiting Time Distribution ◽  
Poisson Stream ◽  
Waiting Time Process ◽  
The Subject ◽  
Effective Service

In [1] the authors dealt with a particular queueing system in which arrivals occurred in a Poisson stream and the probability differential of a service completion was μσn when the queue contained n customers. Much of the theory could not be carried out further analytically for a general σn , which is a purely n-dependent quantity. To carry the analysis further to the extent of finding the “effective” service time and the waiting time distribution when σn is a linear function of n, (which is considered to be rather general and sufficient for practical purposes), constitutes the subject matter of this paper.

Some analyses on the control of queues using level crossings of regenerative processes

1980 ◽  
Vol 17 (3) ◽  
pp. 814-821 ◽  
Author(s):  
J. G. Shanthikumar
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Queueing Systems ◽  
Density Functions ◽  
Waiting Time Distribution ◽  
Regenerative Processes ◽  
Stieltjes Transform ◽  
Expected Number ◽  
Control Of Queues ◽  
Special Case

Some properties of the number of up- and downcrossings over level u, in a special case of regenerative processes are discussed. Two basic relations between the density functions and the expected number of upcrossings of this process are derived. Using these reults, two examples of controlled M/G/1 queueing systems are solved. Simple relations are derived for the waiting time distribution conditioned on the phase of control encountered by an arriving customer. The Laplace-Stieltjes transform of the distribution function of the waiting time of an arbitrary customer is also derived for each of these two examples.

Some analyses on the control of queues using level crossings of regenerative processes

1980 ◽  
Vol 17 (03) ◽  
pp. 814-821 ◽  
Author(s):  
J. G. Shanthikumar
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Queueing Systems ◽  
Density Functions ◽  
Waiting Time Distribution ◽  
Regenerative Processes ◽  
Stieltjes Transform ◽  
Expected Number ◽  
Control Of Queues ◽  
Special Case

Some properties of the number of up- and downcrossings over level u, in a special case of regenerative processes are discussed. Two basic relations between the density functions and the expected number of upcrossings of this process are derived. Using these reults, two examples of controlled M/G/1 queueing systems are solved. Simple relations are derived for the waiting time distribution conditioned on the phase of control encountered by an arriving customer. The Laplace-Stieltjes transform of the distribution function of the waiting time of an arbitrary customer is also derived for each of these two examples.

The stationary work in system of a G/G/1 gradual input queue

1993 ◽  
Vol 30 (1) ◽  
pp. 207-222 ◽  
Author(s):  
Issei Kino ◽  
Masakiyo Miyazawa
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Work Load ◽  
Total Work ◽  
Waiting Time Distribution ◽  
Input Process ◽  
Explicit Formulas ◽  
Input Queue ◽  
Work Input ◽  
Stieltjes Transforms

This paper is devoted to the study of a stationary G/G/1 queue in which work input is gradually injected into the system and the work load is processed at unit rate. First, assuming that the input process is stationary, the key formula for the stationary distribution of work in system is derived by appeal to the waiting time of the associated regular G/G/1 queue. The main contribution of this paper is the derivation of Laplace-Stieltjes transforms (LSTs) for the stationary distributions of work in system and related random variables in terms of integrations with respect to a waiting time distribution of the associated regular queue. The results are exemplified by giving explicit formulas for the LST of total work for M/Ek/1 and M/H2/1. The results generalize the results of Pan et al. (1991) for the M/M/1 gradual input queue.

A queue with Markov-dependent service times

1968 ◽  
Vol 5 (02) ◽  
pp. 461-466
Author(s):  
Gerold Pestalozzi
Keyword(s):  
Steady State ◽  
Generating Function ◽  
Waiting Time ◽  
Service Time ◽  
Queueing System ◽  
Single Channel ◽  
Probability Generating Function ◽  
Average Waiting Time ◽  
Poisson Input ◽  
The Mean

A queueing system is considered where each item has a property associated with it, and where the service time interposed between two items depends on the properties of both of these items. The steady state of a single-channel queue of this type, with Poisson input, is investigated. It is shown how the probability generating function of the number of items waiting can be found. Easily applied approximations are given for the mean number of items waiting and for the average waiting time.

scholarly journals Note sur un modele de file GI/G/1 a service autonome (avec vacances du serveur)

1987 ◽  
Vol 19 (1) ◽  
pp. 289-291 ◽  
Author(s):  
Christine Fricker
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Time Distribution ◽  
Conditional Distribution ◽  
Stochastic Decomposition ◽  
Analytic Method ◽  
Service Time Distribution ◽  
Waiting Time Distribution ◽  
Vacation Model ◽  
The Law

Keilson and Servi introduced in [5] a variation of a GI/G/1 queue with vacation, in which at the end of a service time, either the server is not idle, and he starts serving the first customer in the queue with probability p, or goes on vacation with probability 1 – p, or he is idle, and he takes a vacation. At the end of a vacation, either customers are present, and the server starts serving the first customer, or he is idle, and he takes a vacation. The case p = 1, called the GI/G/1/V queue, was studied analytically by Gelenbe and Iasnogorodski [3] (see also [4]) and then by Doshi [1] and Fricker [2] who obtained stochastic decomposition results on the waiting-time of the nth customer extending the law decomposition result of [3]. Keilson and Servi [5] give a more complete analytic method of treating both the GI/G/1/V model and the Bernoulli vacation model: instead of the waiting time, they use a bivariate process at the service and vacation initiation epochs and the waiting-time distribution is computed as a conditional distribution of the above. In this note the law decomposition result is obtained from a reduction to the GI/G/1/V model with a modified service-time distribution just using the waiting time, with simple path arguments so that by [1] and [2] stochastic decomposition results are valid, which extend the result of [5].

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