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Queueing Theory Essay

786 words - 4 pages

Multiple-Server
Waiting Line
Model
with Poisson
Arrivals and
Exponential
Service Times
Rechell Kaye B. Mosqueda, CPA

Multiple-Server Waiting Line Model
A multiple-server waiting line consists of two
or more servers that are assumed to be
identical in terms of service capability.
For multipleserver
systems,
there are two
typical
queuing
possibilities:

(1) arriving customers wait in a single waiting line
(called a “pooled” or “shared” queue) and then
move to the first available server for processing,
(2) each server has a “dedicated” queue and an
arriving customer selects one of these lines to join
(and typically is not allowed to switch lines).

Multiple-Server ...view middle of the document...

Although Burger Dome would like to serve each customer
immediately, at times more customers arrive than can be handled by the
Burger Dome food service staff. Thus, customers wait in line to place and
receive their orders. Burger Dome is concerned that the methods currently
used to serve customers are resulting in excessive waiting times and a
possible loss of sales. Management wants to conduct a waiting line study to
help determine the best approach to reduce waiting times and improve
service. Suppose that Burger Dome analyzed data on customer arrivals and
concluded that the arrival rate is 45 customers per hour. For a one-minute
period, the arrival rate would be 45 customers/60 minutes = 0.75 customers
per minute. Suppose that Burger Dome studied the order-filling process and
found that a single employee can process an average of 60 customer
orders per hour. On a one-minute basis, the service rate would be 60
customers/60 minutes = 1 customer per minute.

Example: Burger Dome

For an arrival rate of 0.75
customers per minute and a
service rate of 1 customer per
minute for each of the two
servers, (λ = 0.75, µ = 1, k = 2)
we obtain the operating
characteristics:

Example: Burger Dome
The probability
that no units are in
the system:
The average
number of units in
the waiting line:
The average
number of...

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