A taxi cab company has three taxis that operate from the airport. The time it takes for a taxi to take the customer to their destination is exponentially distributed with parameter u. Customers arrive according to a Poisson process with an average of rate 2. If a customer arrives when no taxi is available, they go to another taxi cab company. The taxis always return to their base station at the airport after dropping off a customer without picking up any new customers on their way back. a) Identify the states of the system, arrival and departure rates in each state, and draw the state transition diagram of the system.
b) Derive an expression of the probability that all the taxis are available.
c) What is the probability that an arriving customer goes to another taxi cab company?

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if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!

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