Consider a queueing system with two types of customers. Type 1 customers arrive according to aPoisson process with a mean rate of 7 per hour. Type 2 customers also arrive according to a Poissonprocess with a mean rate of 5 per hour. The system has two servers, both of which serve both typesof customers. For both types, service times have an exponential distribution with a mean of 12minutes. Service is provided on a first-come-first-served basis.a) What is the probability distribution (including its mean) of the time between consecutive arrival ofcustomers of any type?b) When a particular type 2 customer arrives, he finds two type 1 customers there in the process ofbeing served but no other customers in the system. What is the probability distribution (including itsmean) of this type 2 customer's waiting time in the queue?

In queuing theory, the arrival of customers is distributed as Poisson. And the service time provided…

Answered: Consider a queueing system with two…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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