# Forgetting about weekends we arrive at the following

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Unformatted text preview: dges. Each machine requires one toner cartridges which lasts for an exponentially distributed amount of time with mean 6 days. When a toner cartridge is empty it is sent to a repairman who takes an exponential amount of time with mean 1 day to reﬁll it. (a) Compute the stationary distribution. (b) How often are all three printers working? 4.17. Customers arrive at a full-service one-pump gas station at rate of 20 cars per hour. However, customers will go to another station if there are at least two cars in the station, i.e., one being served and one waiting. Suppose that the service time for customers is exponential with mean 6 minutes. (a) Formulate a Markov chain model for the number of cars at the gas station and ﬁnd its stationary distribution. (b) On the average how many customers are served per hour? 4.18. Solve the previous problem for a two-pump self-serve station under the assumption that customers will go to another station if there are at least four cars in the station, i...
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## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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