Problem $520$ points

The magnetic stripe card is used by transit systems across the country. The card is read by units located in

computerized ticket machines and turnstiles. When the rider enters the system, the turnstile read$-$write unit

records the place and time of entry. Surprisingly, the processing of transit riders through the turnstiles is

substantially slower with stripe cards $(20$ passengers$/$minute$)$ than with tokens $(30$ pax$/$minute$).$ The slower

transaction time at the turnstile is due in large part to the process of putting the card into a slot located at the

turnstile and retrieving it$.$

A$.$ Which queueing model $($x$/$y$/$z$)$ would apply to the analysis of a turnstile operating under periods of

moderate passenger demand? Explain.

B$.$ Queueing Performance. For a period in which the passenger arrival rate at a turnstile is $16$ pax$/$minute$,$

compute average length of queue and average wait time for both mag stripe and token turnstiles. Show

your calculations clearly