 Blocking probability in a finite-line sequential-service network

ID: blocking-probability-in-a-finite-line-sequential-service-network

Represent

N

telephone lines by a closed migration process with free-line, operator and automated-service colonies. Accepted arrivals have rate

ν

when a free line exists,

c

operators complete at rate

λ min (k, c)

, and

i

automated calls complete at rate

μ i

D_{c} (k) = \prod_{h = 1}^{k} min (h, c)

and

H_{c} (n) = \sum_{i = 0}^{n} \frac{( ν / λ ) ^{n - i} ( ν / μ ) ^{i}}{D _{c} ( n - i ) i !} .

The product-form stationary distribution of a closed migration process and Poisson arrivals see time averages give the displayed blocking probability. This extends a single-operator model without treating the independent operators as a server with rate

c λ

when fewer than

c

calls are present.

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