queue theory: there are 4 servers, the first two are faster , One service per tw

Question

queue theory: there are 4 servers, the first two are faster , One service per two minutes, and the rest two take more time (three times more). if the interval for customer is 5 minutes at day shift ( from 8 to 8 pm) and 8 minutes at night shift and if there are 2 queue for each tied of server and cars alternately dispatch to each queue answer these questions: 1: car number 15,20,30,50 will be assigned to?? 2: how can we change the configuration of server to be assured the length of each queue remain less than 5?

Explanation / Answer

Faster - server 1 and server 2

Slower - server 3 and server 4

Faster tier takes 2 minutes while slower server takes (2 + 3*2) = 8 minutes.

During daytime, customer arrive every 5 minute and during night time, customer arrive every 8 minutes.

Since cars are arriving every 5 minute (or 8 minutes for night time), therefore only queue1 suffices because this faster queue processes the cars in just 2 minutes. So, by the time new car arrives, both queues are empty. There is no need to put car into slower queue in such situation.

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