$9-3$ Consider the data in Table $9-6.$ This table reports the number of a specific lab test received for processing at an outpatient medical lab over a $10-$day period of time. Based on machine capabilities and staffing, the service rate for the day shift $(7$ AM$-3$ PM$)$ must be constant even though the arrival rate changes during this time period. The system currently operates as a single channel single server system.

a$.$ What service rate do you recommend for the day shift $(7$ AM$-3$ PM$)?$ Remember that the service rate must be greater than the arrival rate. Use queuing parameters to describe this system with different service rates.

b$.$ What are the implications of changing this system from a single server to a multiple server system in which $S=2.$ Show the queuing theory parameters. How would management make this decision?

Table $9-6$ Data on Outpatient Medical Laboratory

$\backslash$table$[[,$Number of lab tests received by day and time$],[$Day $/$ Time,$7-11$ AM$,11-3$ PM$,3-7$ PM$,7-7$ AM$],[1,156,105,44,355],[2,155,110,48,363],[3,160,121,59,390],[4,154,127,32,320],[5,180,127,50,370],[6,170,120,32,322],[7,155,126,30,380],[8,167,129,30,430],[9,148,130,40,320],[10,155,105,35,350],[$Average tests,$160,120,40,360],[$Average per hour,$40,30,10,30],[$Service rate per hour,$60,60,20,40]]$