Question: Question 2 Suppose that a queueing system has three types of customers. Type 1 customer arrive according to a Poisson process with a mean rate

Question 2 Suppose that a queueing system has

Question 2 Suppose that a queueing system has three types of customers. Type 1 customer arrive according to a Poisson process with a mean rate of 5 per hour. Type 2 customer arrive according to a Poisson process with a mean rate of 3 per hour. Type 3 customer also arrive according to a Poisson process with a mean rate of 2 per hour. The system has two servers, both of which serve three types of customers. For all types of customers, all service times are identical which follow an exponential distribution with a mean of 10 minutes. The service is provided on a first-come-first-served basis. (a) What is the probability distribution (including its mean) of the time between consecutive arrivals of customers of any type? [5] (b) When a particular type 2 customer arrives, she finds two type 1 customers there in the process of being served but no other customers in the system. What is the probability distribution (including its mean) of this type 2 customer's waiting time in the queue? [5] (c) Under the condition in (b), what is the probability that the next customer of any type will come after 10 minutes? [10]

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 General Management Questions!

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...

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

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...

There are three types of customers. Type 1, 2, and 3 customers arrive in accordance with independent Poisson processes with respective rate 1 , 2 , and 3 . There are three servers. A type 1 arrival...

\fCHAPTER 14 Server Farms: M/M/k and M/M/k/k In today's high-volume world, almost no websites, compute centers, or call centers consist of just a single server. Instead a \"server farm\" is used. The...

7.21 Consider a two-priority queueing system in which priority class 1 (i.e., high-priority) customers arrive according to a Poisson process with rate two customers per hour and priority class 2...

The next few questions tackle a more realistic design situation. In chapter 2 , a case study explored the formulation of a markov chain model of a call center. In that model, time was represented by...

Due to rising energy prices, the government of World Kingdom (WK) encourages its citizens to install solar panels on their roofs. They offer full or partial funding of solar panel costs to support...

Eureka Enterprises Inc. manufactures bathroom fixtures. The stockholders' equity accounts of Eureka Enterprises Inc., with balances on January 1, 2008, are as follows: Common Stock , $10 stated value...

Marketing control is the process in which organizations examine the consequences of the marketing activities and programs by making appropriate changes and adjustment. a) Explain THREE (3) types of...

3. No endangered species are creatures loved by the timber industry. All spotted owls are endangered species. Th erefore, some spotted owls are not creatures loved by the timber industry. Use the fi...

Nonprobability - not every individual as opportunity to be included which increases the chance that sample is not representative of population. Convenience sample is like finding subjects at the...