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In: Statistics and Probability

Consider an Erlang service system (M / Ek / 1) in which no queue is allowed...

Consider an Erlang service system (M / Ek / 1) in which no queue is allowed to form. Let n = the number of stages of service left in the system, and let pn be the equilibrium probability of being in state n.

(a) Write flow balance equations.

(b) Find an expression for pn, n = 0, 1, ..., k

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Given Data

an Erlang service system (M / Ek / 1) in which no queue is allowed to form.

Let n = the number of stages of service left in the system, and let pn be the equilibrium probability of being in state n

a) Write flow balance equations.

The balance equation is

for n = 0

Where denotes the probability of being in state 0

denotes the probability of being in state 1

denotes the stages arrive per unit time

denotes the stages arrived per unit time

b) Find an expression for pn, n = 0, 1, ..., k

The expression for pn is

c) Find the probability of a busy system.

The probability of a busy system is

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