Module 7: Queuing Theory

Question 1

It is formed when arrivals wait for a service or an opportunity such as the arrival of an accepted gap in a main traffic stream, collection of tolls at a tollbooth, or of parking fees at parking garage

Answer 1

Queue

Question 2

Symbol for the arrival rate

Answer 2

λ

Question 3

Symbol for the departure service rate

Answer 3

µ

Question 4

This queuing is the simplest having deterministic arrivals and departures, and one departure channel

Answer 4

D/D/1 Queuing

Question 5

Queuing that has exponentially distributed arrivals, deterministic departure, and one departure channel

Answer 5

M/D/1 Queuing

Question 6

Queuing that has exponentially distributed arrivals and departure, and one departure channel

Answer 6

M/M/1 Queuing

Question 7

M/M/1 Queuing

Formula for Traffic Intensity

Answer 7

P = λ/µ

Question 8

M/M/1 Queuing

Formula for expected no. of units in the system

Answer 8

E(n) = λ / (µ-λ)
or
E(n) = P / (1-P)

Question 9

M/M/1 Queuing

Formula for expected no. of waiting to be served

Answer 9

E(m) = λ² / (µ) (µ-λ)
or
E(m) = P² / (1-P)
or
E(m) = E(n) x P

Question 10

M/M/1 Queuing

Formula for Average Total Delay

Answer 10

E(v) =1 / (𝜇−λ)

Question 11

M/M/1 Queuing

Formula for average waiting time in queue

Answer 11

E(w) = λ / (𝜇) (𝜇−λ)
or
E(w) = E(v) × 𝑃

Question 12

M/D/1 Queuing

Formula for Traffic Intensity

Answer 12

P = λ/µ

Question 13

M/D/1 Queuing

Formula for expected no. of waiting to be served

Answer 13

E(m) =P² / (2) (1−P)

Question 14

M/D/1 Queuing

Formula for Average Total Delay

Answer 14

E(v) =2-P / (2𝜇)(1−P)

Question 15

M/D/1 Queuing

Formula for average waiting time in queue

Answer 15

E(w) = P / (2𝜇) (1−P)