Stationary Random Processes Associated with Point Processes

1981 ◽  
Author(s):  
Tomasz Rolski
Keyword(s):  
Point Processes ◽  
Random Processes ◽  
Stationary Random Processes

On remaining full busy periods of GI/G/c queues and their relation to stationary point processes

1990 ◽  
Vol 27 (1) ◽  
pp. 232-236 ◽  
Author(s):  
Saeed Ghahramani
Keyword(s):  
Stationary Point ◽  
Busy Period ◽  
Point Processes ◽  
Equilibrium Distribution ◽  
Broad Class ◽  
Random Processes ◽  
Stationary Random Processes ◽  
First Time ◽  
Stationary Point Processes

For a GI/G/c queue, a full busy period is a period commencing when an arrival finds c − 1 customers in the system and ending when, for the first time after that, a departure leaves behind c − 1 customers in the system. We show that given a full busy period is found to be in progress at a random epoch, the remaining full busy period has the equilibrium distribution. Moreover, we demonstrate that this property is typical for a broad class of stationary random processes.

On remaining full busy periods of GI/G/c queues and their relation to stationary point processes

1990 ◽  
Vol 27 (01) ◽  
pp. 232-236 ◽  
Author(s):  
Saeed Ghahramani
Keyword(s):  
Stationary Point ◽  
Busy Period ◽  
Point Processes ◽  
Equilibrium Distribution ◽  
Broad Class ◽  
Random Processes ◽  
Stationary Random Processes ◽  
First Time ◽  
Stationary Point Processes

For a GI/G/c queue, a full busy period is a period commencing when an arrival finds c − 1 customers in the system and ending when, for the first time after that, a departure leaves behind c − 1 customers in the system. We show that given a full busy period is found to be in progress at a random epoch, the remaining full busy period has the equilibrium distribution. Moreover, we demonstrate that this property is typical for a broad class of stationary random processes.

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