Queuing model formulas for a simple single line, single server queuing system
with random arrivals and service times (M/M/1)
(Make changes to yellow cells only)
What are the “units” being served? Planes
What are the time periods? (hours, days, etc.) Hours
What is the arrival rate per time period? 8.5 Planes
What is the service rate per time period? 12 Planes
Queuing model formulas for a simple single line, multiple server queuing system
with random arrivals and service times (M/M/C)
(Make changes to yellow cells only)
IMPORTANT: The formulas are only valid if the cumulative service rate exceeds the arrival rate (c*m > l)
Number of
servers (c)
Probability of zero
planes in the system
(P0)
Average
number of
planes in
system
(Ls)
Average
number of
planes in
line (Lq)
Average
time in
system
(Ws)
Average
time in
line (Wq)
Part c)
The results for the single line, multiple server model show that with two runways, the average number of planes waiting will be 0.801
Part d)
The results for the single line, multiple server model show that with two runways, the average time waiting will be 0.05 hours, or about 3 minutes.
Part a)
Ave. # in system (Ls) 2.43 Planes
Part b)
Ave. time in system (Ws):
Queuing model formulas for a simple single line, single server queuing system
with random arrivals and service times (M/M/1)
(Make changes to yellow cells only)
What are the “units” being served? Customers
What are the time periods? (hours, days, etc.) hours
What is the arrival rate per time period? 11 Customers
What is the service rate per time period? 15 Customers
Part a)
Part b)
Customers have to wait on average 0.18 hours to be checked out. This translates into 0.18*60 = 10.8 minutes.
This number seems a little high. However, before Hector’s decides on whether they want a second checkout register, they
need to:
2. Identify the impact on waiting times.
4. Determine whether the additional costs of staffing a second register are more than covered by the additional profit.
Queuing model formulas for a simple single line, multiple server queuing system
with random arrivals and service times (M/M/C)
(Make changes to yellow cells only)
IMPORTANT: The formulas are only valid if the cumulative service rate exceeds the arrival rate (c*m > l)
Number of
servers (c)
Probability of zero
customers in the
system (P0)
Average
number of
customers
in system
(Ls)
Average
number of
customers
in line (Lq)
Average
time in
system
(Ws)
Average
time in
line (Wq)
Part c)
Part d)
Queuing model formulas for a simple single line, single server queuing system
with random arrivals and service times (M/M/1)
(Make changes to yellow cells only)
What are the “units” being served? Parts
What are the time periods? (hours, days, etc.) hours
What is the arrival rate per time period? 100 Parts
What is the service rate per time period? 150 Parts
Part a)
Ave. # in system (Ls) 1.33 Parts
Part b)
Ave. time in system (Ws):
λ = 4
Arrivals
Probability n
arrivals
Cumulative
probability
Assigned
random numbers
(0 to 100)
Arrivals
10.0733 9%
2 < r < 9 1
30.1954 43%
24 < r < 43 3
43 < r < 63 4
50.1563 79%
63 < r < 79 5
79 < r < 89 6
70.0595 95%
89 < r < 95 7
95 < r < 98 8
90.0132 99%
98 < r < 99 9
Time Period Random no.
Simulated
Arrivals
274.03 4
422.18 1
675.95 4
810.63 1
10 42.99 2
12 2.68 0
14 73.41 4
16 73.79 4
18 22.89 1
0 < r < 2 0
Crew
1