219638
20190317000502.0
0257-0130
10.1007/s11134-016-9480-3
doi
000375790200007
ISI
ARTICLE
The roles of coupling and the deviation matrix in determining the value of capacity in M/M/1/C queues
Dordrecht
2016
Springer Verlag
2016
23
Journal Articles
In 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.
M/M/1/C queue
Coupling
Deviation matrix
Markov chain
Braunsteins, Peter
Univ Melbourne, Sch Math & Stat, Parkville, Vic 3010, Australia
Hautphenne, Sophie
Univ Melbourne, Sch Math & Stat, Parkville, Vic 3010, Australia
255548
249022
Taylor, Peter G.
Univ Melbourne, Sch Math & Stat, Parkville, Vic 3010, Australia
157-179
1-2
Queueing Systems
83
Preprint
314457
Preprint
http://infoscience.epfl.ch/record/219638/files/BraunsteinsHautphenneTaylor2016.pdf
STAT
252136
U10124
oai:infoscience.tind.io:219638
article
SB
GLOBAL_SET
111184
EPFL-ARTICLE-219638
EPFL
PUBLISHED
REVIEWED
ARTICLE