Batch arrival single-server queue with variable service speed and setup time

2017 ◽  
Vol 86 (3-4) ◽  
pp. 241-260 ◽  
Author(s):  
Moeko Yajima ◽  
Tuan Phung-Duc
Keyword(s):  
Setup Time ◽  
Batch Arrival ◽  
Single Server ◽  
Single Server Queue ◽  
Server Queue

scholarly journals A Batch Arrival Single Server Queue with Server Providing General Service in Two Fluctuating Modes and Reneging during Vacation and Breakdowns

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Monita Baruah ◽  
Kailash C. Madan ◽  
Tillal Eldabi
Keyword(s):  
Repair Process ◽  
Batch Arrival ◽  
Single Server ◽  
Single Server Queue ◽  
Numerical Illustration ◽  
Random Breakdown ◽  
Special Cases ◽  
Server Queue ◽  
Service Rates ◽  
General Service

We study the behavior of a batch arrival queuing system equipped with a single server providing general arbitrary service to customers with different service rates in two fluctuating modes of service. In addition, the server is subject to random breakdown. As soon as the server faces breakdown, the customer whose service is interrupted comes back to the head of the queue. As soon as repair process of the server is complete, the server immediately starts providing service in mode 1. Also customers waiting for service may renege (leave the queue) when there is breakdown or when server takes vacation. The system provides service with complete or reduced efficiency due to the fluctuating rates of service. We derive the steady state queue size distribution. Some special cases are discussed and numerical illustration is provided to see the effect and validity of the results.

GeoX/G/1/N Queue with Vacation and Limited Service Discipline

2013 ◽  
Vol 756-759 ◽  
pp. 2470-2474
Author(s):  
Mian Zhang
Keyword(s):  
Queue Length ◽  
Batch Arrival ◽  
Service Discipline ◽  
Single Server ◽  
Single Server Queue ◽  
Arrival Times ◽  
Service Completion ◽  
Server Queue ◽  
Service Times ◽  
Limited Service

We consider a finite butter single server queue with batch arrival, where server serves a limited number of customer before going for vacation (s).The inter arrival times of batches are assumed to be independent and geometrically distribute. The service times and the vacation times of the server are generally distributed and their durations are integral multiples of slots duration. We obtain queue length distributions at service completion, vacation termination and arbitrary epochs.

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