TY - JOUR
T1 - Extension of the loss probability formula to an overloaded queue with impatient customers
AU - Kim, Bara
AU - Kim, Jeongsim
N1 - Funding Information:
We are very grateful to professor Henk Tijms for providing us with the idea that inspired us to write this paper. B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2014R1A2A2A01005831 ). J. Kim’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2014R1A1A4A01003813 ).
Publisher Copyright:
© 2017 Elsevier B.V.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2018/3
Y1 - 2018/3
N2 - We consider a batch arrival MX∕G∕1 queue with impatient customers. The loss probability is expressed in terms of the stationary waiting time distribution for the standard MX∕G∕1 queue with no impatience. But this expression is only applicable when the offered load ρ is less than 1. We give a formula for the loss probability applicable for any values of ρ>0, by proving that the loss probability is analytic in ρ on (0,∞) through a Girsanov-type change of measure.
AB - We consider a batch arrival MX∕G∕1 queue with impatient customers. The loss probability is expressed in terms of the stationary waiting time distribution for the standard MX∕G∕1 queue with no impatience. But this expression is only applicable when the offered load ρ is less than 1. We give a formula for the loss probability applicable for any values of ρ>0, by proving that the loss probability is analytic in ρ on (0,∞) through a Girsanov-type change of measure.
KW - Girsanov-type change of measure
KW - Impatient customers
KW - Loss probability
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U2 - 10.1016/j.spl.2017.10.007
DO - 10.1016/j.spl.2017.10.007
M3 - Article
AN - SCOPUS:85034592459
VL - 134
SP - 54
EP - 62
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
SN - 0167-7152
ER -