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SINGLE-CHANNEL QUEUING MODEL WITH POISSON ARRIVALS AND EXPONENTIAL SERVICE TIMES 459

MANAGEMENT SCIENCE IN ACTION

Ensuring Phone Access to Emergency Services
magine a situation where you have to call the and ran computer simulations using queuing theory.
I emergency services – maybe an emergency However, they quickly realized that the standard use
ambulance for someone having a heart attack, of the exponential distribution was not appropriate.
maybe the police for a road traffic accident, maybe Having analyzed some 4.5 million residential calls
the fire and rescue service to evacuate a burning and found a mean call length of around five minutes
building. You pick up the phone to call and can not they concluded that the exponential distribution of
get a dialling tone. Obviously at the best of times this call times estimated from the mean did not fit the
will be a nuisance but in emergencies it could empirical data well. The prime reason for this was
actually be life threatening. In 2001 AT&T, one the that a small number of total calls, around 6 per cent
world’s largest telecoms companies, found itself in a of the total, were customers using dial-up facilities to
situation where an increasing number of complaints connect to the Internet. These calls had a mean call
were being received from customers about the lack length of around 30 minutes. Using sophisticated
of a dialling tone at certain times of the day. Although techniques, the team obtained a better fitting distri-
not restricted to emergency situations, it was esti- bution that more accurately modelled call length.
mated that this could affect up to 90 life-threatening The results of their modelling allowed AT&T to
situations per day. Initial research indicated that the improve service quality to customers and reduce
problem was occurring mostly during the evening costs by better routing of calls over the network.
when residential phone demand peaks, suggesting
Based on V. Ramaswami, D.Poole, S. Ahn, S. Byers and A. Kaplan,
congestion and queuing in the phone network. The
‘Ensuring Access to Emergency Services in the Presence of Long
team investigating the problem collected call data Internet Dial-up Calls’, Interfaces, 35 5 (Sept–Oct 2005): 411–422.

If the operating characteristics are unsatisfactory in terms of meeting standards
for service, the Dome’s management should consider alternative designs or plans for
improving the queuing operation.

Improving the Queuing Operation
Queuing models often indicate where improvements in operating characteristics are
desirable. However, the decision of how to modify the queuing system configuration
to improve the operating characteristics must be based on the insights and creativity
of the analyst.

Table 11.2 The Probability of n Customers in the System for the Dome Queuing
Problem

Number of Customers Probability
0 0.2500
1 0.1875
2 0.1406
3 0.1055
4 0.0791
5 0.0593
6 0.0445
7 or more 0.1335

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