Transient solution for queue-length distribution of Geometry/G/1 queueing model

2007 ◽  
Vol 22 (1) ◽  
pp. 95-100 ◽  
Author(s):  
Chuanyi Luo ◽  
Yinghui Tang ◽  
Renbin Liu
Keyword(s):  
Queue Length ◽  
Length Distribution ◽  
Queueing Model ◽  
Transient Solution ◽  
Queue Length Distribution

Transient solutions for denumerable-state Markov processes

1994 ◽  
Vol 31 (03) ◽  
pp. 635-645
Author(s):  
Guang-Hui Hsu ◽  
Xue-Ming Yuan
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Queue Length ◽  
Queueing System ◽  
Length Distribution ◽  
Initial Distribution ◽  
Numerical Results ◽  
Transient Solution ◽  
Queue Length Distribution ◽  
Transient Solutions

The algorithm for the transient solution for the denumerable state Markov process with an arbitrary initial distribution is given in this paper. The transient queue length distribution for a general Markovian queueing system can be obtained by this algorithm. As examples, some numerical results are presented.

Transient solutions for denumerable-state Markov processes

1994 ◽  
Vol 31 (3) ◽  
pp. 635-645 ◽  
Author(s):  
Guang-Hui Hsu ◽  
Xue-Ming Yuan
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Queue Length ◽  
Queueing System ◽  
Length Distribution ◽  
Initial Distribution ◽  
Numerical Results ◽  
Transient Solution ◽  
Queue Length Distribution ◽  
Transient Solutions

The algorithm for the transient solution for the denumerable state Markov process with an arbitrary initial distribution is given in this paper. The transient queue length distribution for a general Markovian queueing system can be obtained by this algorithm. As examples, some numerical results are presented.

Analytical solution of finite capacity M/D/1 queues

2000 ◽  
Vol 37 (04) ◽  
pp. 1092-1098
Author(s):  
Olivier Brun ◽  
Jean-Marie Garcia
Keyword(s):  
Queue Length ◽  
Length Distribution ◽  
Point Of View ◽  
Queueing Model ◽  
Finite Capacity ◽  
Computational Point ◽  
Queue Length Distribution ◽  
The Mean ◽  
Mean Queue Length ◽  
Number Of Customers

Although the M/D/1/N queueing model is well solved from a computational point of view, there is no known analytical expression of the queue length distribution. In this paper, we derive closed-form formulae for the distribution of the number of customers in the system in the finite-capacity M/D/1 queue. We also give an explicit solution for the mean queue length and the average waiting time.

Optimal Control for an Mx/G/1 Queue with Two Operation Modes

1997 ◽  
Vol 11 (2) ◽  
pp. 255-265 ◽  
Author(s):  
Alexander Dudin
Keyword(s):  
Optimal Control ◽  
Queue Length ◽  
Length Distribution ◽  
Queueing Model ◽  
Explicit Dependence ◽  
Modes Of Operation ◽  
Queue Length Distribution ◽  
Stationary Queue Length ◽  
Switchover Times ◽  
Stationary Queue Length Distribution

The controlled Mx/G/1-type queueing model with two modes of operation is considered. The modes are characterized by different service time distributions and input rates. The switchover times are imposed in the model. The embedded stationary queue-length distribution and the explicit dependence of operation criteria on switchover levels are derived.

Analytical solution of finite capacity M/D/1 queues

2000 ◽  
Vol 37 (4) ◽  
pp. 1092-1098 ◽  
Author(s):  
Olivier Brun ◽  
Jean-Marie Garcia
Keyword(s):  
Queue Length ◽  
Length Distribution ◽  
Point Of View ◽  
Queueing Model ◽  
Finite Capacity ◽  
Computational Point ◽  
Queue Length Distribution ◽  
The Mean ◽  
Mean Queue Length ◽  
Number Of Customers

Although the M/D/1/N queueing model is well solved from a computational point of view, there is no known analytical expression of the queue length distribution. In this paper, we derive closed-form formulae for the distribution of the number of customers in the system in the finite-capacity M/D/1 queue. We also give an explicit solution for the mean queue length and the average waiting time.

On the steady-state solution of the M/G/2 queue

1979 ◽  
Vol 11 (01) ◽  
pp. 240-255 ◽  
Author(s):  
Per Hokstad
Keyword(s):  
Steady State ◽  
General Solution ◽  
Laplace Transform ◽  
Queue Length ◽  
Joint Distribution ◽  
Length Distribution ◽  
Steady State Solution ◽  
Queue Length Distribution ◽  
The Difference ◽  
Number Of Customers

The asymptotic behaviour of the M/G/2 queue is studied. The difference-differential equations for the joint distribution of the number of customers present and of the remaining holding times for services in progress were obtained in Hokstad (1978a) (for M/G/m). In the present paper it is found that the general solution of these equations involves an arbitrary function. In order to decide which of the possible solutions is the answer to the queueing problem one has to consider the singularities of the Laplace transforms involved. When the service time has a rational Laplace transform, a method of obtaining the queue length distribution is outlined. For a couple of examples the explicit form of the generating function of the queue length is obtained.

scholarly journals New Approach for Finding Basic Performance Measures of Single Server Queue

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Siew Khew Koh ◽  
Ah Hin Pooi ◽  
Yi Fei Tan
Keyword(s):  
Stationary State ◽  
Queue Length ◽  
Length Distribution ◽  
Cumulative Distribution ◽  
System Capacity ◽  
Interarrival Time ◽  
Single Server ◽  
Single Server Queue ◽  
Queue Length Distribution ◽  
Server Queue

Consider the single server queue in which the system capacity is infinite and the customers are served on a first come, first served basis. Suppose the probability density functionf(t)and the cumulative distribution functionF(t)of the interarrival time are such that the ratef(t)/1-F(t)tends to a constant ast→∞, and the rate computed from the distribution of the service time tends to another constant. When the queue is in a stationary state, we derive a set of equations for the probabilities of the queue length and the states of the arrival and service processes. Solving the equations, we obtain approximate results for the stationary probabilities which can be used to obtain the stationary queue length distribution and waiting time distribution of a customer who arrives when the queue is in the stationary state.

scholarly journals Approximation of The Queue Length Distribution of General Queues

ETRI Journal ◽  
1994 ◽  
Vol 15 (3) ◽  
pp. 35-45 ◽  
Author(s):  
Kyu-Seok Lee ◽  
Hong Shik Park
Keyword(s):  
Queue Length ◽  
Length Distribution ◽  
Queue Length Distribution
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