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. A bank has 4 tellers with different service rates, i.e., teller 1 averages 10 customers/hour,...

. A bank has 4 tellers with different service rates, i.e., teller 1 averages 10 customers/hour, teller 2 averages 15 customers/hour, teller 3 averages 12 customers/hour, and teller 4 averages 10 customers/hour (all with exponential service times). Assume that there are 20 seats in the lobby, and any customer arriving to a fully-occupied lobby leaves.

a. If the system is modeled as a Markov chain, what is the total number of states?

b. What is the average time between departing customers if tellers 1, 3, and 4 are busy?

c. What is the average time between departing customers when 5 customers are waiting?

Math   Statistics-And-Probability   
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