A multiple server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 4 customers per hour and an average service time of 18 minutes per customer.The minimum number of servers required to avoid an overloaded system is:
A)1
B)2
C)3
D)4
E)5

Question

Quizplus · Accepted Answer

First, we need to calculate the traffic intensity, which is given by:
ρ = λ/μk

where λ is the arrival rate, μ is the service rate (which is the inverse of the service time), and k is the number of servers.

Substituting the given values, we get:
ρ = (4/60)/(1/18 * k)
ρ = 0.12k

For the system not to become overloaded, ρ should be less than 1. Using this condition, we can determine the minimum number of servers required.

0.12k < 1
k < 8.333

Since the number of servers cannot be a decimal, we round it up to the nearest integer, which gives us k = 2. Therefore, we need a minimum of two servers to avoid an overloaded system.

A Multiple Server Queuing System with a Poisson Arrival Rate