Consider a self-service model in which the customer is also the server.Note that this corresponds to having an infinite number of servers available.Customers arrive according to a Poisson process with parameter $\lambda$ ,and service times have an exponential distribution with parameter $\mu$ .
(a)Find L_q and W_q.
(b)Construct the rate diagram for this queueing system.
(c)Use the balance equations to find the expression for P_n in terms of P₀.
(d)Find P₀.
(e)Find L and W.

Question

Consider a self-service model in which the customer is also the server.Note that this corresponds to having an infinite number of servers available.Customers arrive according to a Poisson process with parameter

\lambda

,and service times have an exponential distribution with parameter

\mu

.
(a)Find L_q and W_q.
(b)Construct the rate diagram for this queueing system.
(c)Use the balance equations to find the expression for P_n in terms of P₀.
(d)Find P₀.
(e)Find L and W.

Quizplus · Accepted Answer

The Answer of Consider a self-service model in which the customer is also the server.Note that this corresponds to having an infinite number of servers available.Customers arrive according to a Poisson process with parameter $\lambda$,and service times have an exponential distribution with parameter $\mu$. (a)Find L_q and W_q. (b)Construct the rate diagram for this queueing system. (c)Use the balance equations to find the expression for P_n in terms of P₀. (d)Find P₀. (e)Find L and W.

Consider a Self-Service Model in Which the Customer Is Also λ\lambdaλ

Consider a Self-Service Model in Which the Customer Is Also $\lambda$