b) A telephone exchange multiplexes 64 Kb/s voice calls onto a 256 Kb/s trunk line (therefore the line will hold at most four calls). New calls have an exponentially distributed inter-arrival process, with a mean of 20 seconds, and the call holding time is exponentially distributed with a mean of 60 seconds. (i) Draw a diagram of a Markov Chain which models the system, labelling the state transitions with their rates where appropriate. (ii) What is the necessary condition for stability of this system? A

Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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b) A telephone exchange multiplexes 64 Kb/s voice calls onto a 256 Kb/s trunk
line (therefore the line will hold at most four calls). New calls have an
exponentially distributed inter-arrival process, with a mean of 20 seconds,
and the call holding time is exponentially distributed with a mean of 60
seconds.
(i) Draw a diagram of a Markov Chain which models the system, labelling the
state transitions with their rates where appropriate.
(ii) What is the necessary condition for stability of this system? A
Transcribed Image Text:b) A telephone exchange multiplexes 64 Kb/s voice calls onto a 256 Kb/s trunk line (therefore the line will hold at most four calls). New calls have an exponentially distributed inter-arrival process, with a mean of 20 seconds, and the call holding time is exponentially distributed with a mean of 60 seconds. (i) Draw a diagram of a Markov Chain which models the system, labelling the state transitions with their rates where appropriate. (ii) What is the necessary condition for stability of this system? A
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