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Unformatted text preview: ther taxis are present.
However, if an arriving person does not ﬁnd a taxi waiting he leaves to ﬁnd
alternative transportation. (a) Find the proportion of arriving customers that
get taxis. (b) Find the average number of taxis waiting.
4.33. Queue with impatient customers. Customers arrive at a single server at
rate and require an exponential amount of service with rate µ. Customers
waiting in line are impatient and if they are not in service they will leave at
rate independent of their position in the queue. (a) Show that for any > 0
the system has a stationary distribution. (b) Find the stationary distribution
in the very special case in which = µ.
4.34. Customers arrive at the Shortstop convenience store at a rate of 20 per
hour. When two or fewer customers are present in the checkout line, a single
clerk works and the service time is 3 minutes. However, when there are three
or more customers are present, an assistant comes over to bag up the groceries
and reduces the service time to 2 minutes. Assuming the service times are
exponentially distributed, ﬁnd the stationary dist...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.
 Spring '10
 DURRETT
 The Land

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