An M/M/1 Queue System with Single Working Vacation and Impatient Customers

2013 ◽  
pp. 767-776
Author(s):  
Xiao-ming Yu ◽  
De-an Wu ◽  
Lei Wu ◽  
Yi-bing Lu ◽  
Jiang-yan Peng
Keyword(s):  
Impatient Customers ◽  
Working Vacation ◽  
Queue System

scholarly journals Phase-Type Arrivals and Impatient Customers in Multiserver Queue with Multiple Working Vacations

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Cosmika Goswami ◽  
N. Selvaraju
Keyword(s):  
Blocking Probability ◽  
Death Process ◽  
Impatient Customers ◽  
Working Vacation ◽  
Multiple Working Vacations ◽  
Phase Type ◽  
Working Vacations ◽  
The One ◽  
Vacation Period ◽  
Stationary Probability Vector

We consider a PH/M/c queue with multiple working vacations where the customers waiting in queue for service are impatient. The working vacation policy is the one in which the servers serve at a lower rate during the vacation period rather than completely ceasing the service. Customer’s impatience is due to its arrival during the period where all the servers are in working vacations and the arriving customer has to join the queue. We formulate the system as a nonhomogeneous quasi-birth-death process and use finite truncation method to find the stationary probability vector. Various performance measures like the average number of busy servers in the system during a vacation as well as during a nonvacation period, server availability, blocking probability, and average number of lost customers are given. Numerical examples are provided to illustrate the effects of various parameters and interarrival distributions on system performance.

scholarly journals Multi-server system with single working vacation

2009 ◽  
Vol 33 (7) ◽  
pp. 2967-2977 ◽  
Author(s):  
Chuen-Horng Lin ◽  
Jau-Chuan Ke
Keyword(s):  
Working Vacation ◽  
Multi Server ◽  
Server System
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