Mathematics, 24.04.2020 04:30 mmk4

Consider a call center with three identical agents (servers) and four phone lines. Call arrivals follow a Poisson process with rate 2 per minute. An arriving call that finds all lines busy is lost (blocked). Call processing times are i. i.d., exponentially distributed with mean 1 minute. An admitted call that finds all agents busy will wait until getting service, occupying a phone line. Model this system as a CTMC.

1.Find the long-term throughput of the system (the rate of served customers leaving the system).

2.Find the average waiting time (in queue) among those who are served. Find the average number of calls in the entire system.

Answers: 3

Show answers

Answers

Answer from: bridgettebach

1. the rate of served customer leaving the system is 13/9

2. average waiting time in queue is 4/9 minutes

average number of calls in the entire system is 26/9 = 2.889 calls

Step-by-step explanation:

hello,

The queuing model is a 3 channel or server model. We will use the following notations in solving the question;

M= Number of servers which is 3

λ= average arrival rate = 2 minutes

μ = average service rate at each server = 1 minute

please note that the rate of served customers leaving the system is the same as the average rate a customers spends in waiting line and being served (or in other words the average time spent in the system)

W_s = the rate of served calls leaving the system

W_q = average waiting time in queue.

L = average number of calls in the system.

To solve this we must first find the probability, P that there are 0 call in the system. please see the first attached file for the formula to find P.

Thus we have;

$P=\frac{1}{[\sum_{n=0}^{n=2}\frac{1}{n!} (\frac{2}{1} )^n] +\frac{1}{3!}(\frac{2}{1} )^3 \frac{(3)(1)}{(3)(1)- 2} }$

$P=\frac{1}{[1+2+2] + \frac{8}{6}(3) }$

$P=\frac{1}{5+4} = \frac{1}{9}$

2. we will find the average number of calls in the entire system for this will be used for find the rate of served customers leaving the system. please see the second attached file for the formula for the average number of calls in the entire system.

$L=\frac{(2)(1)(\frac{2}{1} )^3}{(3-1)! ((3)(1)- 2)^2} (\frac{1}{9} ) + (\frac{2}{1})$

$L=\frac{16}{2} (\frac{1}{9} ) +(2 ) = \frac{26}{9} = 2.889 \ \ $calls$$

Next we find the rate of served customers leaving the system.

please see the third attached file for the formula of the rate of served customers leaving the system.

$W_s=\frac{\frac{26}{9} }{2} = \frac{13}{9} \ $minutes$$

finally we find the average waiting time in queue.

please see the fourth attached file for the formula of the average waiting in queue.

$W_q=\frac{13}{9} - 1 = \frac{4}{9} \ $minutes$$

Consider a call center with three identical agents (servers) and four phone lines. Call arrivals fol

Answer from: Quest

a) one student is chosen from classroom a, then a student is chosen from classroom b.

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b. this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes. this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes. this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes. this makes them dependent events.

Answer from: Quest

2.2°

step-by-step explanation:

let θ = the angle of elevation.

tanθ =77/2020

tanθ = 0.038 12

θ = tan⁻¹0.038 12

θ = 2.2°

Another question on Mathematics

Mathematics, 21.06.2019 16:30

We have enough material to build a fence around a station that has a perimeter of 180 feet the width of the rectangular space must be 3 1/4 feet what must the length be

Answers: 1

Answer

Mathematics, 21.06.2019 18:00

Name each raycalculation tip: in ray "ab", a is the endpoint of the ray.

Answers: 2

Answer

Mathematics, 21.06.2019 21:20

Find the missing variable for a parallelogram: a = latex: 28in^2 28 i n 2 h = b = 6.3 in (1in=2.54cm)

Answers: 3

Answer

Mathematics, 21.06.2019 23:00

Assume that there is a 11% rate of disk drive failure in a year. a. if all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. if copies of all your computer data are stored on four independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?

Answers: 2

Answer

You know the right answer?

Consider a call center with three identical agents (servers) and four phone lines. Call arrivals fol...

Questions