Consider a petrol pump which has a single petrol dispensing unit. Customers arrive there in accordance with a Poisson process having rate minutes. An arriving customer enters the petrol pump only if there are two or less customers in the petrol pump, otherwise he/she leaves the petrol pump without taking the petrol (at any point of time a maximum of three customers are present in the petrol pump). Successive service times of the petrol dispensing unit are independent exponential random variables having mean 1/2 minutes. Let X denote the average number of customers in the petrol pump in the long run. Then E(X) is equal to
Part BCSIR NET June 2024finite-capacity-queue-must-renormalise
Finite capacity queue must renormalise
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The chapter behind this: Markov chains: classification and stationary behaviour — free to read
From Limit Theorems and Markov Chains › Markov chains: classification of states, stationary distributions