Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 54-62 |
| Number of pages | 9 |
| Journal | Statistics and Probability Letters |
| Volume | 134 |
| DOIs | |
| Publication status | Published - 2018 Mar 1 |
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Keywords
- Girsanov-type change of measure
- Impatient customers
- Loss probability
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
Cite this
Extension of the loss probability formula to an overloaded queue with impatient customers. / Kim, Bara; Kim, Jeongsim.
In: Statistics and Probability Letters, Vol. 134, 01.03.2018, p. 54-62.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Extension of the loss probability formula to an overloaded queue with impatient customers
AU - Kim, Bara
AU - Kim, Jeongsim
PY - 2018/3/1
Y1 - 2018/3/1
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
UR - http://www.scopus.com/inward/record.url?scp=85034592459&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85034592459&partnerID=8YFLogxK
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 -