Logistics Management 344
Queuing Theory, Simulation, Chi^2 Test & Linear
Programming
1. Queuing Theory
Key terms:
Wq Time in the queue (e.g. time waiting to be serviced)
Ws Time in service (e.g. time spent at the counter/washbay)
W Time in the system (e.g. time spent in the premises)
Lq Number of vehicles in the queue (e.g. number of vehicles waiting to be
served)
Ls Number of vehicles in the service (e.g. number of vehicles at the washbay)
L Number of vehicles in the system (e.g. number of vehicles in the premises)
p Utilization factor
P0 Probability is ‘idle’
Kendall-Lee notation:
a Nature of the interarrival times
b Nature of the service times
c Number of service points
d Queuing rules
e Number of customers allowable in the system
f Number of customers in the calling population
GD=FIFO
Base assumptions for a M/M/1/GD/∞/∞ queuing model:
1. Queuing rules follow FIFO – first in first out
2. No balking or reneging
, 3. Interarrival times are mutually independent & follow the exponential
distribution with lambda being known
4. Service times are mutually independent & follow the exponential
distribution with mu being known
5. Calling population in infinitely large & there is no space constraint
6. Lambda < mu
Base assumptions for a M/M/3/GD/∞/∞ queuing model:
1. Queuing rules follow FIFO – first in first out
2. No balking or reneging
3. Interarrival times are mutually independent & follow the exponential
distribution with lambda being known
4. Service times are mutually independent & follow the exponential
distribution with mu being known
5. Calling population in infinitely large & there is no space constraint
6. Lambda < mu
Base assumptions for a M/M/1/GD/9/9 queuing model:
1. Queuing rules follow FIFO – first in first out
2. No balking or reneging
3. Service times are mutually independent & follow the exponential
distribution with mu being known
4. The calling population in finite
5. Arrival times follow the poisson distribution
, Calculations/formulas:
*NB do all calculations using below formulas on excel to determine values!
*Determine probability that ‘1’ or more of the scanners are busy P = ’1’ – P0
*Average number of ships being serviced at any time = L – Lq
M/M/1/GD/∞/∞
M/M/3/GD/∞/∞
Queuing Theory, Simulation, Chi^2 Test & Linear
Programming
1. Queuing Theory
Key terms:
Wq Time in the queue (e.g. time waiting to be serviced)
Ws Time in service (e.g. time spent at the counter/washbay)
W Time in the system (e.g. time spent in the premises)
Lq Number of vehicles in the queue (e.g. number of vehicles waiting to be
served)
Ls Number of vehicles in the service (e.g. number of vehicles at the washbay)
L Number of vehicles in the system (e.g. number of vehicles in the premises)
p Utilization factor
P0 Probability is ‘idle’
Kendall-Lee notation:
a Nature of the interarrival times
b Nature of the service times
c Number of service points
d Queuing rules
e Number of customers allowable in the system
f Number of customers in the calling population
GD=FIFO
Base assumptions for a M/M/1/GD/∞/∞ queuing model:
1. Queuing rules follow FIFO – first in first out
2. No balking or reneging
, 3. Interarrival times are mutually independent & follow the exponential
distribution with lambda being known
4. Service times are mutually independent & follow the exponential
distribution with mu being known
5. Calling population in infinitely large & there is no space constraint
6. Lambda < mu
Base assumptions for a M/M/3/GD/∞/∞ queuing model:
1. Queuing rules follow FIFO – first in first out
2. No balking or reneging
3. Interarrival times are mutually independent & follow the exponential
distribution with lambda being known
4. Service times are mutually independent & follow the exponential
distribution with mu being known
5. Calling population in infinitely large & there is no space constraint
6. Lambda < mu
Base assumptions for a M/M/1/GD/9/9 queuing model:
1. Queuing rules follow FIFO – first in first out
2. No balking or reneging
3. Service times are mutually independent & follow the exponential
distribution with mu being known
4. The calling population in finite
5. Arrival times follow the poisson distribution
, Calculations/formulas:
*NB do all calculations using below formulas on excel to determine values!
*Determine probability that ‘1’ or more of the scanners are busy P = ’1’ – P0
*Average number of ships being serviced at any time = L – Lq
M/M/1/GD/∞/∞
M/M/3/GD/∞/∞
