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.

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

1999 ◽  
Vol 36 (3) ◽  
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.

Analysis of the M x/G/1 queue by N-policy and multiple vacations

1994 ◽  
Vol 31 (02) ◽  
pp. 476-496
Author(s):  
Ho Woo Lee ◽  
Soon Seok Lee ◽  
Jeong Ok Park ◽  
K. C. Chae
Keyword(s):  
Performance Measures ◽  
Queue Length ◽  
Time Distribution ◽  
Queueing System ◽  
Random Variables ◽  
System Size ◽  
The Other ◽  
Waiting Time Distribution ◽  
Multiple Vacations ◽  
Linear Cost

We consider an Mx /G/1 queueing system with N-policy and multiple vacations. As soon as the system empties, the server leaves for a vacation of random length V. When he returns, if the queue length is greater than or equal to a predetermined value N(threshold), the server immediately begins to serve the customers. If he finds less than N customers, he leaves for another vacation and so on until he finally finds at least N customers. We obtain the system size distribution and show that the system size decomposes into three random variables one of which is the system size of ordinary Mx /G/1 queue. The interpretation of the other random variables will be provided. We also derive the queue waiting time distribution and other performance measures. Finally we derive a condition under which the optimal stationary operating policy is achieved under a linear cost structure.

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).

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.

Sign in / Sign up

Export Citation Format

Share Document