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What is the average number of customers waiting at the rank

Question:

Taxis and customers arrive at a taxi rank in accordance with two independent homogeneous Poisson processes with intensities an hour and λ1 = 4 an hour, λ2 = 3 respectively. Potential customers who find two waiting customers do not wait for service, but leave the rank immediately. (Groups of customers who will use the same taxi are considered to be one customer.) On the other hand, arriving taxis who find two taxis waiting leave the rank as wel

A transport company has 4 trucks of the same type. There

The times between failures of a truck (lifetime) is exponential with parameter The repair times are exponen with parameter All life and repair times are assumed to be independent.

l. What is the average number of customers waiting at the rank?

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## Q : Applying the optional stopping theorem

whichever occurs first. By using suitable martingales and applying the optional stopping theorem, determine