The basic models template provided , Queuing Model Template Many of a bank's customers use its automatic teller machine to transact business after normal banking hours During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute This can be modeled using a Poisson distribution Each customer spends an average of 90 seconds completing his or her transactions Transaction time is exponentially distributed Determine The average time customers spend at the machine, including waiting in line and completing transactions The probability that a customer will not have to wait upon arriving at the automatic teller machine The average number waiting to use the machine Extend your analysis of the ATM machine queuing system (from the problem above) as follows The original problem had an arrival on average one every other minute , i e on average 120 seconds apart Evaluate the system characteristics for the following time between arrivals in seconds 240, 180, 120, 110, 100, 95, 93, 92, 91 5, 91 Why can't we evaluate the system with arrivals on average 90 seconds apart What would happen to the long run average queue time if the time between arrivals was less than 90 seconds chart that plots the average time in queue (on the vertical axis) vs the server utilization on the horizontal axis Interpret this chart (Note The time between arrivals values, and the utilization values that result from them, are not evenly spaced Do not plot them as evenly spaced on your chart You will need to use a scatterplot type of chart ( with lines and markers option) in Excel, A local utility has a cu Single Server Waiting Line Model (M M 1) Exponential time between arrivals, exponential service times Arrival rate Average time between arrivals Service rate Average service time l 1 l m 1 m 10 0 1000 12 0 0833 System Utilization Probability system is empty r P0 0 8333 0 1667 Average number of customers in queue Lq 4 1667 Average number of customers in system Ls 5 0000 Average time in queue per customer Wq 0 4167 Average time in system per customer Ws 0 5000 n P( 4 ) P(

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The basic models template provided , Queuing Model Template Many of a bank's customers use its automatic teller machine to transact business after normal banking

The basic models template provided , Queuing Model Template

Many of a bank's customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Each customer spends an average of 90 seconds completing his or her transactions. Transaction time is exponentially distributed. Determine:

The average time customers spend at the machine, including waiting in line and completing transactions.
The probability that a customer will not have to wait upon arriving at the automatic teller machine.
The average number waiting to use the machine.

Extend your analysis of the ATM machine queuing system (from the problem above) as follows: The original problem had an arrival on average "one every other minute", i.e. on average 120 seconds apart. Evaluate the system characteristics for the following time between arrivals in seconds: 240, 180, 120, 110, 100, 95, 93, 92, 91.5, 91. Why can't we evaluate the system with arrivals on average 90 seconds apart? What would happen to the long run average queue time if the time between arrivals was less than 90 seconds? chart that plots the average time in queue (on the vertical axis) vs. the server utilization on the horizontal axis. Interpret this chart. (Note: The time between arrivals values, and the utilization values that result from them, are not evenly spaced. Do not plot them as evenly spaced on your chart. You will need to use a "scatterplot" type of chart ("with lines and markers" option) in Excel, .
A local utility has a cu

Single Server Waiting Line Model (M/M/1) Exponential time between arrivals, exponential service times Arrival rate Average time between arrivals Service rate Average service time l= 1/l = m= 1/m = 10 0.1000 12 0.0833 System Utilization Probability system is empty r= P0 = 0.8333 0.1667 Average number of customers in queue Lq = 4.1667 Average number of customers in system Ls = 5.0000 Average time in queue per customer Wq = 0.4167 Average time in system per customer Ws = 0.5000 n= P( 4 ) = P(