Customers arrive according to a poisson process

Reference no: EM131130501

Customers arrive according to a Poisson process with rate A outside a bank where there are two automated teller machines (ATM). The two ATMs are not identical. We estimate that 30% of the customers use only ATM no. 1, while 20% of the customers use only ATM no. 2. The other customers (50%) make use of either ATM indifferently. The service times at each ATM are independent exponential random variables with parameter μ. Finally, there is space for a single waiting customer. We define the states

(a) Write the balance equations of the system. Do not solve them.

(b) Calculate, in terms of the limiting probabilities,

(i) the variance of the number of customers who are waiting to use an ATM,

(ii) the average time that an arbitrary customer, who enters the system and wishes to use ATM no. 2, will spend in the system.

Reference no: EM131130501

Questions Cloud

Why might the company refuse to split its shares to make : The share price of BRKA has never been spilt. Why might the company refuse to split its shares to make them more affordable to average investors?

What is economic rationale for regulating pharmaceuticals : What is the economic rationale for regulating pharmaceuticals? How much regulation should occur? Who thinks this regulation is positive? Who thinks it is negative?

How would this affect measured velocity : Velocity and ATMs. Suppose the introduction of ATMs led households to hold less of their wealth as deposits in banks or savings and loans.

What should the management of sports products : What should the management of Sports Products, Inc., pursue as its overriding goal? Why? Does the firm appear to have an agency problem? Explain. Evaluate the firm's approach to pollution control. Does it seem to be ethical? Why might incurring the e..

Customers arrive according to a poisson process : Customers arrive according to a Poisson process with rate A outside a bank where there are two automated teller machines (ATM). The two ATMs are not identical. We estimate that 30% of the customers use only ATM no.

How change is influenced in the organization : How the culture was formed and the effects that its culture has on the organization's outcomes and effectiveness?- how new members of the organization are socialized?

Will these companies have issues involving customer privacy : What are the implications for those companies that bid for the chance to have exclusive advertising featured on their webpage? Is this practice based on the information exchange or some other type of consumer behavior?

What is the growth rate of real output : If the growth rate of money is 10 percent per year, annual inflation is 7 percent, and the growth rate of velocity is 1 percent per year, what is the growth rate of real output?

Queueing system in which ordinary customers arrive : We consider a queueing system in which ordinary customers arrive according to a Poisson process with rate λ and are served in a random time having an exponential distribution, with parameter μ, by either of two servers.

User Account

All Pages