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HMWK 5
Problems from the Text
Ch. 6, Page 409: 12, 13, 22
Problems not from the textbook
1. According to a Poisson process at rate
λ
= 20 per day, a company buys units (100 share
blocks) of stock
A
and holds on to each unit, independently of other units, for
H
days,
where
H
has an exponential distribution with
E
(
H
) = 60 (days).
Assume that initially (time
t
= 0) no units of stock A are held.
(a) Compute the expected number of units held at times
t
= 20,
t
= 50 and
t
= 90 days.
(b) What is the longrun average number of units held by the company?
(c) Repeat (a), (b) when
H
has a uniform distribution on (40
,
80).
2.
Printer with jams
: Jobs arrive to a computer printer according to a Poisson process at
rate
λ
. Jobs are printed one at a time requiring iid printing times that are exponentially
distributed with rate
μ
. Jobs wait in a FIFO queue before entering service.
Additionally, independently, the printer jams at times that form a Poisson process at rate
γ
. Whenever a jam ocurrs the job being printed (if any) is removed, and the printer
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 Fall '08
 Whitt
 Operations Research

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