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

question 1

Essay

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 λ\lambda ,and service times have an exponential distribution with parameter μ\mu .
(a)Find Lq and Wq.
(b)Construct the rate diagram for this queueing system.
(c)Use the balance equations to find the expression for Pn in terms of P0.
(d)Find P0.
(e)Find L and W.


Definitions:

Indifference Curve

A graph showing different combinations of two goods that provide equal satisfaction and utility to a consumer.

Marginal Rates of Substitution

The speed at which a buyer is prepared to sacrifice one item for another while keeping their satisfaction constant.

Bads

Are items that people do not desire to have, opposite to goods, which have a negative impact on utility when consumed.

Indifference Curves

Graphical representations in microeconomics showing different bundles of goods between which a consumer is indifferent.

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