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462 CHAPTER 11 QUEUING MODELS

Multiple-Channel Queuing Model with Poisson Arrivals
11.3
and Exponential Service Times

You may be familiar with A multiple-channel queuing system consists of two or more service channels that are
multiple-channel systems assumed to be identical in terms of service capability. In the multiple-channel
that also have multiple
queues. The queuing system, arriving units wait in a single queue and then move to the first available
model in this section has channel to be served. The single-channel Dome operation can be expanded to a two-
multiple channels, but channel system by opening a second service channel. Figure 11.3 shows a diagram of
only a single queue. the Dome two-channel queuing system.
Operating characteristics
for a multiple-channel In this section we present formulas that can be used to determine the steady-state
system are better when a operating characteristics for a multiple-channel queuing system. These formulas are
single queue, rather than applicable if the following conditions exist.
multiple queues, is used.
1 The arrivals follow a Poisson probability distribution.
2 The service time for each channel follows an exponential probability distribution.
3 The mean service rate is the same for each channel.
4 The arrivals wait in asingle queueand then move to the first open channel for service.

Operating Characteristics
The following formulas can be used to compute the steady-state operating character-
istics for multiple-channel queueing systems, where:
¼ the mean arrivals rate for the system
¼ the mean service rate for each channel
k ¼ the number of channels
1 The probability that no units are in the system:

1
P 0 ¼ (11:11)
k 1 n ð = Þ k k
P ð = Þ
þ
n¼0 n! k! k

Figure 11.3 The Dome Two-Channel Waiting Line

System

Channel 1

Server A
Customer
Customer Customer Goes Leaves
Arrivals to Next Open After Order
Channel Is Filled
Queue
Channel 2

Server B

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