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1. QUEUING,
LIFO, FIFO
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2. Thompson’s Mining & Smelting Co.
Bank Ground of The study
The company is planning to increase it’s
production rate. The company’s refinery at
Wekusko is under discussion, where
production is planned to increase to 35000
tons per week. Mr. Brian Walker, the
superintendent of the plant had carried
out a study at the plant to ensure for
achieving the target. An analysis of
operation was carried out for maximizing
the use of available resources.
Facts of the Wekusko Plant
1. Location : California
2. Resources Avaialble

3. a) Three Yard Shovels -
3Nos. Located at different areas
b) 20 Ton Trucks 12 Nos.
c) Primary Crusher - 1 No.
3) Opearating schedule of
the Plant
a) Shift – I for 8
hours:
2 shovels along with 4 trucks /
shovel.
b) Shift – II for 8 hours
1 Shovel along with 5 Trucks
4. Trucks could not be switch over from
one shovel to another.
5. The plant is working 5 days a week

4. 6. Capacity of Primary Crusher : 9600
Tons per Shift (480 Trucks Load)
Objectives
The Company’s objective of increased
production to 35000 Tons per week could
be achieved by exploring 7000 tons of ore
per day from all the shovels. whereas the
Crusher is having the capacity of 9600
tons per shift.
Criteria
1. It could be possible with the
following by 100% utilizing the
crusher to the best of it’s capacity,
which is possible only by reducing
the waiting time for crusher, for

5. which, the waiting time of the
trucks at each shovel as tabulated
below, needs to be eliminated.
S.
No.
Shovel Waiting
time for
Trucks at
shovel in
every round
trip (in
Minutes)
Extra Cost
per Hour
in US$ *
1 1 1.17 1.36
2 2 -0.41 1.00
* Computation of Extra Cost Per Hour
In shift – I at shovel - I, the truck remains idle
for 1.17 min for every round trip, which comes
to 10.74 min per hour (60/6.54*1.17) resulting
into extra cost of US$ 1.36 per hour.
In shift – I at Shovel - II, the shovel remains
idle for 0.41 min for every round trip, which

6. comes to 3.03 min per hour (60/8.12*0.41)
resulting into extra cost of US$ 1.00 per hour.

7. End Result
Under the above situation the Crusher
is supplied with 10601 Tons of Material
(60/8.12*8*4*20+60/6.54*8*4*20)
against its capacity of 9600 Tons per
Shift. It is not out of place to mention
here that there is the scope of
reducing the transportation cost &
Shovel Cost as attributable to the
1001 Tons to line up with the capacity
of Crusher.
Parameters Used in Calculations
A queuing model is defined with formulae
that make use of the variables described
in the following.

8. QUEUING MODEL CHARACTERISTICS
Primary Queuing Model
Characteristics
A queuing model is defined in terms of the
following primary characteristics. For use
in calculations, these characteristics are
expressed using the letter that is indicated
in brackets following the name of the
characteristic.
• Request Arrival Rate (a). Service
requests arrive according to one of

9. four patterns: steady, irregular,
regular, or random.
• Service Distribution Rate (s). The
mean number of requests that are
processed within a time period.
• Utilization (u). The intensity of the
traffic. That is, the request arrival rate
divided by the service rate.
• Number of Servers (c). The
number of servers that can process
the request. The number of tellers on
duty affects the length of the line. A
server in this case may not be the
physical server, but may be a critical

10. subcomponent, depending on what is
being modelled.
• Queue Discipline. How queued
requests are processed, which affects
the standard deviation calculation.
Examples are: first-in-first-out (FIFO),
last-in-first-out (LIFO), and priority
ordered. This technique assumes FIFO
queues in all cases.
Variables in Queuing Model
Formulae
The primary queuing model
characteristics are common in the
model formulae. In addition, the

11. following variables may be used
depending on the queuing model.
• Average number of waiting
requests (w),
• Average number in the system (S),
• Average waiting time (Tw),
• Average time in system, i.e.,
response time (Ts),
• Delay due to queuing (D),
• Number of requests or clients (K),
• Probability that all servers are busy
(P(c)),
• Probability that there are K
requests in the system (P(K)),
• Probability that there is no delay
(P(0)),

12. • Erlang-B (B(c,U)),
• Erlang-C (C(c,U)),
• Erlang moment (m).
The formulae used to calculate these
values depend on the type of queue
and the type of distribution. More
complex queues, for example multiple
server queues, require use of more of
these values.

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