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Rensselaer
Electrical, Computer, and Systems Engineering Department
ECSE 4500 Probability for Engineering Applications
Recitation 6
Wednesday March 3, 2010
Waiting time at a restaurant
A certain restaurant has been found to have the following joint distribution for the waiting time
for service for a newly arriving customer and the total number of customers including the new
arrival. Let
W
be a random variable representing the continuous waiting time for a newly arriving
customer, and let
N
be a discrete random variable representing the total number of customers.
The joint distribution function is then given as,
F
W,N
(
w,n
)=
⎧
⎪
⎪
⎨
⎪
⎪
⎩
0
,n
<
0
or
w<
0
,
(1
−
exp
−
w/μ
0
)
n
10
,
0
≤
n
≤
5
,w
≥
0
,
(1
−
exp
−
w/μ
0
)
5
10
+(1
−
exp
−
w/μ
1
)
¡
n
−
5
10
¢
,
5
<n<
10
≥
0
,
(1
−
exp
−
w/μ
0
)
5
10
−
exp
−
w/μ
1
)
¡
5
10
¢
,
10
≤
n, w
≥
0
,
where the parameters
μ
i
satisfy
0
<μ
0
1
. Note that this choice of the parameters means that
waiting times are longer when the number of customers is large.
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This note was uploaded on 04/15/2010 for the course ECSE 4500 taught by Professor Woods during the Spring '08 term at Rensselaer Polytechnic Institute.
 Spring '08
 WOODS

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