000219638 001__ 219638
000219638 005__ 20190317000502.0
000219638 0247_ $$2doi$$a10.1007/s11134-016-9480-3
000219638 022__ $$a0257-0130 000219638 02470$$2ISI$$a000375790200007 000219638 037__$$aARTICLE
000219638 245__ $$aThe roles of coupling and the deviation matrix in determining the value of capacity in M/M/1/C queues 000219638 260__$$aDordrecht$$bSpringer Verlag$$c2016
000219638 269__ $$a2016 000219638 300__$$a23
000219638 336__ $$aJournal Articles 000219638 520__$$aIn an M/M/1/C queue, customers are lost when they arrive to find C customers already present. Assuming that each arriving customer brings a certain amount of revenue, we are interested in calculating the value of an extra waiting place in terms of the expected amount of extra revenue that the queue will earn over a finite time horizon [0, t]. There are different ways of approaching this problem. One involves the derivation of Markov renewal equations, conditioning on the first instance at which the state of the queue changes; a second involves an elegant coupling argument; and a third involves expressing the value of capacity in terms of the entries of a transient analogue of the deviation matrix. In this paper, we shall compare and contrast these approaches and, in particular, use the coupling analysis to explain why the selling price of an extra unit of capacity remains the same when the arrival and service rates are interchanged when the queue starts at full capacity.
000219638 6531_ $$aM/M/1/C queue 000219638 6531_$$aCoupling
000219638 6531_ $$aDeviation matrix 000219638 6531_$$aMarkov chain
000219638 700__ $$aBraunsteins, Peter$$uUniv Melbourne, Sch Math & Stat, Parkville, Vic 3010, Australia
000219638 700__ $$0249022$$aHautphenne, Sophie$$g255548$$uUniv Melbourne, Sch Math & Stat, Parkville, Vic 3010, Australia
000219638 700__ $$aTaylor, Peter G.$$uUniv Melbourne, Sch Math & Stat, Parkville, Vic 3010, Australia
000219638 773__ $$j83$$k1-2$$q157-179$$tQueueing Systems
000219638 8564_ $$s314457$$uhttps://infoscience.epfl.ch/record/219638/files/BraunsteinsHautphenneTaylor2016.pdf$$yPreprint$$zPreprint
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000219638 937__ $$aEPFL-ARTICLE-219638 000219638 973__$$aEPFL$$rREVIEWED$$sPUBLISHED
000219638 980__ aARTICLE