UNIVERSITY OF SOUTHERN CALIFORNIA, FALL 2008
1
EE 550: Problem Set
#
5
Due: Wednesday Oct. 13, 2008
I. B
OOK
P
ROBLEM
3.14
II. J
ACKSON
N
ETWORK
Consider a simple Jackson network consisting of two queues in tandem. The input to the first queue is Poisson with rate
λ
, and departures from this queue enter the second queue. There are no other arrival processes. Service times in both queues
are i.i.d. exponential with rate
μ
, where
λ < μ
. Recall that we use the Kleinrock independence approximation, so that service
times of the same packet in the two queues are independent. Let
(
N
1
, N
2
)
represent the state of the system (representing the
number of packets currently in node
1
and
2
).
a) Suppose
(
N
1
, N
2
) = (1
,
1)
, so that there is exactly one packet in each queue. The next transition corresponds to a “single
event.” List the possible single events.
b) Assuming the state in part (a), what is the expected time to the next transition?
c) Is the process
N
1
(
t
)
, treated alone, reversible? Is
N
2
(
t
)
reversible?
d) Show that the
2
d process
(
N
1
(
t
);
N
2
(
t
))
is not reversible, even though in steady state the current number of packets in
node
1
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 Fall '08
 Neely
 Continuoustime Markov process, total reward, steady state probabilities, current number

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