Unformatted text preview: tates give the
number of customers in the system, with a or b indicating there is one customer
at a or b respectively. Show that this system is time reversible. Set ⇡ (2) = c
and solve to ﬁnd the limiting probabilities in terms of c.
4.37. At present the Economics department and the Sociology department each
have one typist who can type 25 letters a day. Economics requires an average 156 CHAPTER 4. CONTINUOUS TIME MARKOV CHAINS of 20 letters per day, while Sociology requires only average of 15. Assuming
Poisson arrival and exponentially distributed typing times ﬁnd (a) the average
queue length and average waiting time in each departments (b) the average
overall waiting time if they merge their resources to form a typing pool.
4.38. Consider an M/M/s queue with no waiting room. In words, requests for
a phone line occur at a rate . If one of the s lines is free, the customer takes
it and talks for an exponential amount of time with rate µ. If no lines are free,
the customer goes away never to come back. Find the stationary distribution.
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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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