An Optimum Control of a Batch Arrival Queue with Second Optional Service and Setup tiyie under Bernoulli Vaction Schedule
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Date
2012
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Abstract
All M'/G/l iiueiteiiig system with s e e o iid op tion al serv ice (SOS)is stud ied iitider Aipolicy an d
lienwuHi Vacatioti. The system remains id le until the qu eu e size r e a ch e s or ex c e ed s N (> I).
When the qu eu e size r e a ch e s at leitst\, the server may begin his setup op eration with
p robability s o r tnay start the serv ice with p robability ( l-s). The serv er provides two p h a s e s o f
h eterog etieou s services, o f which, first p h a s e o f serv ice is essen tia l attd secon d p h a s e o f
serv ice is opiiotial. I v soon as the first essen tial serv ice (FES) o f a unit is com p leted , the
custouter tnay lea v e the systetn with p robability (l-r) o r tnay immediately opt fo r SOS with
p robability r, Whetieverthe serv ice o f ea ch unit is completed, th e se rv er will h a v e th e option
o f lahitig v acaliotifliernoulli). Thus a customer com p letes his service, by utidergoing F E S
alone, the serv er may ta k e a vacatioti with prob ab ility p/orstays id le o r cotititiue th e next
serv ice to the new cu stom er ifatiy ,with p robability (l-p ij. I f th e customer who fin ish e s F E S
p ro c e ed s to SOS them th e se rv er may ta k e vacation at th e end o f SOS with p ro b a b ility p 2 o r
Slavs idle o r continues with th e F E S fo r the new customer*with probahilitv (l-p :) a cco rd in g
as the system is empty o r having customers in the system. The qu eu e size distribution at a
rand om ep o ch is o b ta in ed f o r this m od el using SVT an d various p a rticu la r ca ses a r e
deduced. Furth er various p e r fo rm a n c e m easu res an d the optimum mattag em ent policy a re
also derived.