REVISITING JOINT STATIONARY DISTRIBUTION IN TWO FINITE CAPACITY QUEUES OPERATING IN PARALLEL

2017 ◽  
Keyword(s):  
Stationary Distribution ◽  
Finite Capacity ◽  
Finite Capacity Queues ◽  
Joint Stationary Distribution

scholarly journals Stationary solution to the fluid queue fed by an M/M/1 queue

2002 ◽  
Vol 39 (2) ◽  
pp. 359-369 ◽  
Author(s):  
N. Barbot ◽  
B. Sericola
Keyword(s):  
Stationary Solution ◽  
Stationary Distribution ◽  
Generating Functions ◽  
The State ◽  
Finite Capacity ◽  
Fluid Queue ◽  
Analytic Expression ◽  
Joint Stationary Distribution

We consider an infinite-capacity buffer receiving fluid at a rate depending on the state of an M/M/1 queue. We obtain a new analytic expression for the joint stationary distribution of the buffer level and the state of the M/M/1 queue. This expression is obtained by the use of generating functions which are explicitly inverted. The case of a finite capacity fluid queue is also considered.

scholarly journals Stationary solution to the fluid queue fed by an M/M/1 queue

2002 ◽  
Vol 39 (02) ◽  
pp. 359-369 ◽  
Author(s):  
N. Barbot ◽  
B. Sericola
Keyword(s):  
Stationary Solution ◽  
Stationary Distribution ◽  
Generating Functions ◽  
The State ◽  
Finite Capacity ◽  
Fluid Queue ◽  
Analytic Expression ◽  
Joint Stationary Distribution

We consider an infinite-capacity buffer receiving fluid at a rate depending on the state of an M/M/1 queue. We obtain a new analytic expression for the joint stationary distribution of the buffer level and the state of the M/M/1 queue. This expression is obtained by the use of generating functions which are explicitly inverted. The case of a finite capacity fluid queue is also considered.

The Mk/G/∞ batch arrival queue by heterogeneous dependent demands

1994 ◽  
Vol 31 (03) ◽  
pp. 841-846
Author(s):  
Gennadi Falin
Keyword(s):  
Linear Function ◽  
Stationary Distribution ◽  
Random Variables ◽  
Dimensional Vector ◽  
Transient Solution ◽  
General Service Times ◽  
Joint Stationary Distribution ◽  
Number Of Customers ◽  
General Service ◽  
Server System

Choi and Park [2] derived an expression for the joint stationary distribution of the number of customers of k types who arrive in batches at an infinite-server system of M/M/∞ type. We propose another method of solving this problem and extend the result to the case of general service times (not necessarily independent). We also get a transient solution. Our main result states that the k- dimensional vector of the number of customers of k types in the system is a certain linear function of a (2 k – 1)-dimensional vector whose coordinates are independent Poisson random variables.

Scale functions of Lévy processes and busy periods of finite-capacity M/GI/1 queues

2004 ◽  
Vol 41 (4) ◽  
pp. 1145-1156 ◽  
Author(s):  
Parijat Dube ◽  
Fabrice Guillemin ◽  
Ravi R. Mazumdar
Keyword(s):  
Closed Form ◽  
Lévy Processes ◽  
Busy Period ◽  
Exit Time ◽  
Levy Processes ◽  
Finite Capacity ◽  
Scale Functions ◽  
Period Distribution ◽  
Finite Capacity Queues ◽  
Time Theory

In this paper we use the exit time theory for Lévy processes to derive new closed-form results for the busy period distribution of finite-capacity fluid M/G/1 queues. Based on this result, we then obtain the busy period distribution for finite-capacity queues with on–off inputs when the off times are exponentially distributed.

Fluid Model Driven by an M/M/1 Queue with Set-Up and Close-Down Period

2014 ◽  
Vol 513-517 ◽  
pp. 3377-3380
Author(s):  
Fu Wei Wang ◽  
Bing Wei Mao
Keyword(s):  
Stationary Distribution ◽  
Solution Method ◽  
Fluid Model ◽  
Model Driven ◽  
Buffer Content ◽  
The Laplace Transform ◽  
Matrix Geometric Solution ◽  
The Mean ◽  
Joint Stationary Distribution ◽  
Set Up

The fluid model driven by an M/M/1 queue with set-up and close-down period is studied. The Laplace transform of the joint stationary distribution of the fluid model is of matrix geometric structure. With matrix geometric solution method, the Laplace-Stieltjes transformation of the stationary distribution of the buffer content is obtained, as well as the mean buffer content. Finally, with some numerical examples, the effect of the parameters on mean buffer content is presented.

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