Analysis of the Sojourn Time Distribution for M/GL/1 Queue with Bulk-Service of Exactly Size L

2018 ◽  
Vol 20 (4) ◽  
pp. 1503-1514
Author(s):  
Miaomiao Yu ◽  
Yinghui Tang
Keyword(s):  
Sojourn Time ◽  
Time Distribution ◽  
Sojourn Time Distribution ◽  
Bulk Service

On the time a Markov chain spends in a lumped state

1997 ◽  
Vol 34 (02) ◽  
pp. 340-345
Author(s):  
Tommy Norberg
Keyword(s):  
Markov Chain ◽  
State Space ◽  
Continuous Time ◽  
Sojourn Time ◽  
Time Distribution ◽  
Sojourn Time Distribution

The sojourn time that a Markov chain spends in a subset E of its state space has a distribution that depends on the hitting distribution on E and the probabilities (resp. rates in the continuous-time case) that govern the transitions within E. In this note we characterise the set of all hitting distributions for which the sojourn time distribution is geometric (resp. exponential).

A BMAP/SM/1 queueing system with Markovian arrival input of disasters

1999 ◽  
Vol 36 (03) ◽  
pp. 868-881
Author(s):  
Alexander Dudin ◽  
Shoichi Nishimura
Keyword(s):  
Sojourn Time ◽  
Queue Length ◽  
Time Distribution ◽  
Queueing System ◽  
Queuing System ◽  
Complicated System ◽  
Sojourn Time Distribution ◽  
Negative Arrivals

Disaster arrival in a queuing system with negative arrivals causes all customers to leave the system instantaneously. Here we obtain a queue-length and virtual waiting (sojourn) time distribution for the more complicated system BMAP/SM/1 with MAP input of disasters.

scholarly journals Analysis of a Single-Sever Queue with Disasters and Repairs Under Bernoulli Vacation Schedule

2016 ◽  
Vol 4 (6) ◽  
pp. 547-559
Author(s):  
Jingjing Ye ◽  
Liwei Liu ◽  
Tao Jiang
Keyword(s):  
Performance Measures ◽  
Generating Functions ◽  
Sojourn Time ◽  
Time Distribution ◽  
Busy Period ◽  
Balance Equations ◽  
Sojourn Time Distribution ◽  
The Mean ◽  
System Length ◽  
Number Of Customers

AbstractThis paper studies a single-sever queue with disasters and repairs, in which after each service completion the server may take a vacation with probabilityq(0≤q≤1), or begin to serve the next customer, if any, with probabilityp(= 1− q). The disaster only affects the system when the server is in operation, and once it occurs, all customers present are eliminated from the system. We obtain the stationary probability generating functions (PGFs) of the number of customers in the system by solving the balance equations of the system. Some performance measures such as the mean system length, the probability that the server is in different states, the rate at which disasters occur and the rate of initiations of busy period are determined. We also derive the sojourn time distribution and the mean sojourn time. In addition, some numerical examples are presented to show the effect of the parameters on the mean system length.

On the time a Markov chain spends in a lumped state

1997 ◽  
Vol 34 (2) ◽  
pp. 340-345 ◽  
Author(s):  
Tommy Norberg
Keyword(s):  
Markov Chain ◽  
State Space ◽  
Continuous Time ◽  
Sojourn Time ◽  
Time Distribution ◽  
Sojourn Time Distribution

The sojourn time that a Markov chain spends in a subset E of its state space has a distribution that depends on the hitting distribution on E and the probabilities (resp. rates in the continuous-time case) that govern the transitions within E. In this note we characterise the set of all hitting distributions for which the sojourn time distribution is geometric (resp. exponential).

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