Question: (Queue with impatient customers). Customers arrive at a single server at rate [1] and require an exponential amount of service with rate . Customers waiting

(Queue with impatient customers). Customers arrive at a single server at rate

[1] and require an exponential amount of service with rate

. Customers waiting in line are impatient and if they are not in service they will leave at rate ı independent of their position in the queue.

(a) Show that for anyı > 0 the system has a stationary distribution.

(b) Find the stationary distribution in the very special case in which

ı D

.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Essentials Of Stochastic Processes Questions!

Q:

It was early June 2010, and two months had passed since Heather Larson had been granted exclusive Canadian distribution rights to the Nutrifusion product. She had been very busy trying to develop the...

Q:

Queue with impatient customers. Customers arrive at a single server at rate and require an exponential amount of service with rate . Customers waiting in line are impatient and if they are not in...

Q:

Fast Pass is used for what type of attractions? Multiple Choice The newest attractions The most popular attractions Customers can chose the attraction All attractions use Fast Pass The least popular...

Q:

Macro quiz...well explained answers only 3.1 Exercise 4.1 Packets arrive to a communication node with a single output link according to a Poisson Process. Give the Kendall notation for the following...

Q:

A service counter employs one server who can serve 11 customers per hour. Customers arrive at the counter at the rate of 9 per hour. Both service rate and arrival rate follow a Poisson distribution....

Q:

A service counter employs one server who can serve 11 customers per hour. Customers arrive at the counter at the rate of 9 per hour. Both service rate and arrival rate follow a Poisson distribution....

Q:

Characteristics of Queuing Systems and Models In a queuing system, customers enter a waiting line, receive service when their turn comes ( possibly waiting in more lines as they proceed through the...

Q:

1 The time spent in a line or queue is a function of all of the following, except A . the queue configuration and discipline B . the waiting costs C . the rate at which the flow units are processed...

Q:

1 The time spent in a line or queue is a function of all of the following, except A . the queue configuration and discipline B . the waiting costs C . the rate at which the flow units are processed...

Q:

1 The time spent in a line or queue is a function of all of the following, except A . the queue configuration and discipline B . the waiting costs C . the rate at which the flow units are processed...

Q:

1 The time spent in a line or queue is a function of all of the following, except A . the queue configuration and discipline B . the waiting costs C . the rate at which the flow units are processed...

Q:

A sample of two printed circuit boards is selected without replacement from a batch. Describe the (ordered) sample space for each of the following batches: (a) The batch contains 90 boards that are...

Q:

Estimate the yearly heat production due to the Earths present 40 K content, assuming B - decay is the dominant mode of radioactive decay (Q= 1.32 MeV/atom decayed). How does this compare with the...

Q:

Portfolio manager, Kris Gaines, needs to develop an investment portfolio for their conservative clients. Their task is to determine the proportion of the portfolio to invest in each of the five...

Q:

How can intellectual property rights be protected in China?