SCM 300 ASU EXAM 2 Questions and Answers
Average number of customers in a single server model
P = Lambda over U
LQ = P^ - P
EX: Lambda = 1.5, U = 3, P = ?, LQ = ?
1. = 0.5 so P = 0.5
0.5^ - 0.5 = 0..5 = 0.5
LQ = 0.5
Be able to calculate what % of time will server be busy in 2,3,4,6 server model
λ = arrival rate
μ\muμ = service rate per server
ccc = number of servers
ρ\rhoρ = overall server utilization (i.e., how busy the system is collectively)
If ρ≥1\rho ≥ 1ρ≥1, the system is overloaded — customers arrive faster than they
can be served.
If ρ<1\rho < 1ρ<1, the system is stable, and you can do deeper analysis like wait
time, queue length, etc.
ρ = λ / (c × μ) = 10 / (2×5) = 1.0
Read from table - what % of time is system empty in single server model
P0 = 1 - P
ρ=λμ\rho = \frac{\lambda}{\mu}ρ=μλ is the utilization (i.e., % of time server is
busy)
λ (arrival rate)μ (service rate)ρ = λ/μ% Time System is Empty (P₀) 2 4 0.5 1 - 0.5 =
0.5 → 50%
, What % of customers served immediately in a 2-server model
Find the probability that a customer does not have to wait — i.e., is served
immediately upon arrival.
Let’s assume:
λ = 4 customers/hour (arrival rate)
μ = 3 customers/hour/server (each server can serve 3 per hour)
c = 2 servers
ρ=c⋅μλ = 4/ 2 * 3 =4/6 = 0.667
This means the system is busy about 66.7% of the time.
In 2 server model, what is probability of more than 2 cust in line, exactly one cust
in line
If Lambda and Mu are given you should be able to calculate▪ Probability of being
served immediately▪ Probability of exactly 1 customer in line
In a single server, what % of time the server will be busy
arrival rate / service rate or ρ=λ/u
What time customer spend in line?
Wq= p / u(1 - p)
first calculate P: P = 6/8 = 0.75
wq = 0.75/ 8(1 - 0.75) = 0. = 0.375
0.375 x 60 = 22.5 mins
What time customer spends in system?
Wq= p / u(1 - p)
first calculate P: P = 6/8 = 0.75
Average number of customers in a single server model
P = Lambda over U
LQ = P^ - P
EX: Lambda = 1.5, U = 3, P = ?, LQ = ?
1. = 0.5 so P = 0.5
0.5^ - 0.5 = 0..5 = 0.5
LQ = 0.5
Be able to calculate what % of time will server be busy in 2,3,4,6 server model
λ = arrival rate
μ\muμ = service rate per server
ccc = number of servers
ρ\rhoρ = overall server utilization (i.e., how busy the system is collectively)
If ρ≥1\rho ≥ 1ρ≥1, the system is overloaded — customers arrive faster than they
can be served.
If ρ<1\rho < 1ρ<1, the system is stable, and you can do deeper analysis like wait
time, queue length, etc.
ρ = λ / (c × μ) = 10 / (2×5) = 1.0
Read from table - what % of time is system empty in single server model
P0 = 1 - P
ρ=λμ\rho = \frac{\lambda}{\mu}ρ=μλ is the utilization (i.e., % of time server is
busy)
λ (arrival rate)μ (service rate)ρ = λ/μ% Time System is Empty (P₀) 2 4 0.5 1 - 0.5 =
0.5 → 50%
, What % of customers served immediately in a 2-server model
Find the probability that a customer does not have to wait — i.e., is served
immediately upon arrival.
Let’s assume:
λ = 4 customers/hour (arrival rate)
μ = 3 customers/hour/server (each server can serve 3 per hour)
c = 2 servers
ρ=c⋅μλ = 4/ 2 * 3 =4/6 = 0.667
This means the system is busy about 66.7% of the time.
In 2 server model, what is probability of more than 2 cust in line, exactly one cust
in line
If Lambda and Mu are given you should be able to calculate▪ Probability of being
served immediately▪ Probability of exactly 1 customer in line
In a single server, what % of time the server will be busy
arrival rate / service rate or ρ=λ/u
What time customer spend in line?
Wq= p / u(1 - p)
first calculate P: P = 6/8 = 0.75
wq = 0.75/ 8(1 - 0.75) = 0. = 0.375
0.375 x 60 = 22.5 mins
What time customer spends in system?
Wq= p / u(1 - p)
first calculate P: P = 6/8 = 0.75
