Question
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
(c) Find the probability of a busy system.
Solutions
Expert Solution
Answer:
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
as
c) Find the probability of a busy system.
The probability of a busy system is
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