image/svg+xml
customer
arrival time
service time
Standard assumptions
- Curse of dimensionality
state:
Higher dimensional Markov models
Computational approach to
“rate in = rate out” equations
Truncate an infinite number of equations
Algebraic formulation
Higher dimensional Markov models
Classical analysis: M/M/n system
- Throughout this talk, we use
For sufficiently large t
Key challenge:
No longer independent Poisson
We start with a discrete service-time distribution:
Number in system X(t)
This suggests
for some quantile
cross-covariances
.
where
Remark:
Iglehart 1965
Borovkov 1967
M/G/
Implication:
G/G/
Factory Physics (Hopp/Spearman 2011) proposes Sakasegawa:
Suggested approximation:
We seek the smallest
search over n yields
search over n yields
12am
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1am
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1
1.2
1.4
1.6
Manhattan 2006, health.ny.gov
310 arrivals per week
our data
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