Sojourn Time Analysis for Processor Sharing Loss Queuing System with Service Interruptions and MAP Arrivals

2016 ◽  
pp. 406-417 ◽  
Author(s):  
Konstantin Samouylov ◽  
Eduard Sopin ◽  
Irina Gudkova
Keyword(s):  
Sojourn Time ◽  
Queuing System ◽  
Processor Sharing ◽  
Time Analysis ◽  
Service Interruptions

scholarly journals Processor-sharing and random-service queues with semi-Markovian arrivals

2005 ◽  
Vol 42 (02) ◽  
pp. 478-490
Author(s):  
De-An Wu ◽  
Hideaki Takagi
Keyword(s):  
Waiting Time ◽  
Sojourn Time ◽  
Time Distribution ◽  
Arrival Process ◽  
Interarrival Time ◽  
Size Distributions ◽  
Processor Sharing ◽  
Queue Size ◽  
Mean Waiting Time ◽  
The Mean

We consider single-server queues with exponentially distributed service times, in which the arrival process is governed by a semi-Markov process (SMP). Two service disciplines, processor sharing (PS) and random service (RS), are investigated. We note that the sojourn time distribution of a type-lcustomer who, upon his arrival, meetskcustomers already present in the SMP/M/1/PS queue is identical to the waiting time distribution of a type-lcustomer who, upon his arrival, meetsk+1 customers already present in the SMP/M/1/RS queue. Two sets of system equations, one for the joint transform of the sojourn time and queue size distributions in the SMP/M/1/PS queue, and the other for the joint transform of the waiting time and queue size distributions in the SMP/M/1/RS queue, are derived. Using these equations, the mean sojourn time in the SMP/M/1/PS queue and the mean waiting time in the SMP/M/1/RS queue are obtained. We also consider a special case of the SMP in which the interarrival time distribution is determined only by the type of the customer who has most recently arrived. Numerical examples are also presented.

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.

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