Question: Consider a single-server queuing system where customers arrive according to a Poisson process with rate , service times are exponential with rate , and customers

Consider a single-server queuing system where customers arrive according to a Poisson process with rate λ, service times are exponential with rate μ, and customers are served in the order of their arrival. Suppose that a customer arrives and finds (n-1) others in the system. Let X denote the number of customers in the system at the moment that customer departs. Find the probability mass function of X, i.e., P[X=k], k=0,1,2.

 

Step by Step Solution

★★★★★

3.60 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

From the given information The customers arrive according to a Poisson proce... View full answer

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 Operating System Questions!

Q:

The following scores represent the number of children in a group of 20 households: a. Calculate the mode, median, and mean from the scores. b. Rearrange the scores into a simple frequency...

Q:

Find a, b, c and d if (a) (b) (c) (d) a b b-c 3 1 2 2

Q:

Consider a queue to which customers arrive according to a Poisson process with rate per hour. Suppose that the queue has two servers. Each customer who arrives at the queue counts the length r of...

Q:

55. Consider a single server queuing system where customers arrive according to a Poisson process with rate , service times are exponential with rate , and customers are served in the order of their...

Q:

55. Consider a single server queuing system where customers arrive according to a Poisson process with rate , service times are exponential with rate , and customers are served in the order of their...

Q:

Consider a single server queuing system where customers arrive according to a Poisson process with rate , service times are exponential with rate , and customers are served in the order of their...

Q:

Consider a single server queuing system where customers arrive according to a Poisson process with rate , service times are exponential with rate , and customers are served in the order of their...

Q:

55. Consider a single server queuing system where customers arrive according to a Poisson process with rate , service times are exponential with rate , and customers are served in the order of their...

Q:

Consider a single server queuing system where customers arrive according to a Poisson process with rate , service times are exponential with rate , and customers are served in the order of their...

Q:

Consider an n-server parallel queuing system where customers arrive according to a Poisson process with rate , where the service times are exponential random variables with rate , and where any...

Q:

Table -1-Cash flow Estimation Plant 1 Net Income Depreciation (Straight- tine) Net Cash Flow Plant 2 Net Income Depredation {Straight- line) Net Cash Flow Year 0 $1,000,000 Year 1 Year 2 Year 4 Year...

Q:

What do you think of Tiffanys decision to not sell diamonds online? What do you think of?

Q:

A colleague has drafted the following letter appealing to fellow employees to join the company s Unite Way Campaign Committee. He is unhappy with the letter and has sked you to revise it . a ) List...

Q:

(a) Discuss the performance of reactors in series of four reactors and justify your analysis using one specific example. (b) Calculate the concentrations of reactant and product for time intervals of...

Q:

What is the rate of reaction in a Batch Culture system? If the growth of microorganisms follows the Monods Model, then interpret the expressions in (3.1) and (3.2) below: (10 marks) dS RV = v dt...

Q:

(a) Explain the analysis of chemical reaction taking piace in four equal-reaction volumes and also in four different-reaction volumes in series given space time, initial and final concentrations. (b)...

Q:

Ben Limited has a 31 December year end. Employees work a 5 day week and are entitled to 20 paid working days of vacation per annum. Employee statistics are as follows: Number of employees : 50 000...

Q:

A catalytic chemical reaction given in (A3.1) that was run at 3.5 atm and 120C in a PER unit that contained 10ce catalys and 20 L/lir of partially converted product of pure uureacted A was analysed...

Q:

Which of the following statements is correct?Underwriting is a process by which the FED purchase new securities directly from the issuing company and resell them to the investors.If you just...

Q:

Consider a queueing system with two types of customers. Type 1 customers arrive according to a Poisson process with a mean rate of 5 per hour. Type 2 customers also arrive according to a Poisson...

Q:

Consider a single-server queuing system for which the interarrival times are exponentially distributed. A customer who arrives and finds the server busy joins the end of a single queue. Service times...

Q:

Consider a single-server queuing system for which the interarrival times are exponentially distributed. A customer who arrives and finds the server busy joins the end of a single queue. Service times...

Q:

7. Consider a single-server queuing system with FIFO service discipline and let X(t) be the number of customers in the system (including the customer in service). A simulation run for 180 minutes...

Q:

Consider a single-server queuing system. If the arrival rate is 44 units per hour, and each customer takes 30 seconds on average to be served, what is the average time in the system to include...

Q:

Consider a single-server queuing system. A customer arrives every .6 minutes. It takes the cashier 20 seconds on average to cash out a customer. If you were the manager you should: A. Add more...