In a waiting line situation, arrivals occur at a rate of 2 per minute, and the service times average 18 seconds.*Please help me find F,G,H. Please show formulas!a.What is λ?2 per minb. What is μ?1/18*60=3.33Traffic intensity= λ/μ = 2/3.33= 0.618 seconds or 3.33 per minute c.Find probability of no units in the system.# units in the system= 1-traffic intensity = 1-0.6= 0.4 d.Find average number of units in the system.Average # units in system= λ/μ-λ= 2/3.33-2= 1.5 … 2 e.Find average time in the waiting line.Average time in the waiting line= λ2/μ (μ-λ)= 22/3.33(3.33-2)= 0.903 f.Find average time in the system. g.Find probability that there is one person waiting. h.Find probability an arrival will have to wait.

Given that λ = 2 μ = 1/18 *60 = 3.333

Answered: f. Find average time in the system.…

f. Find average time in the system. g. Find probability that there is one person waiting. h. Find probability an arrival will have to wait.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

In a waiting line situation, arrivals occur at a rate of 2 per minute, and the service times average 18 seconds.

*Please help me find F,G,H. Please show formulas!

a.	What is λ? 2 per min
b.	What is μ? 1/1860=3.33 Traffic intensity= λ/μ = 2/3.33= 0.6 18 seconds or 3.33 per minute*
c.	Find probability of no units in the system. # units in the system= 1-traffic intensity = 1-0.6= 0.4
d.	Find average number of units in the system. Average # units in system= λ/μ-λ= 2/3.33-2= 1.5 … 2
e.	Find average time in the waiting line. Average time in the waiting line= λ²/μ (μ-λ)= 2²/3.33(3.33-2)= 0.903
f.	Find average time in the system.
g.	Find probability that there is one person waiting.
h.	Find probability an arrival will have to wait.

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