The communication center's call pattern is modeled by a Poisson process,$$with an average of $20$ calls per hour. To ensure efficient handling of these calls,$$the center has implemented a systematic checking procedure. They review$$the call queue at $15-$minute intervals, starting from the top of each hour $($e$.$g$.,00$:$00,00$:$15,00$:$30,00$:$45,$ etc.$).$ If there are new calls waiting, they are$$addressed collectively. In the absence of any waiting calls, the team prepares$$for the next interval