arrival rate
service rate
system utilization = = 10/12 = 0.833
please upvote if this helps
Customers arrive at a suburban ticket outlet at the rate of 10 per hour on Monday...
Waiting lines Customers walk in at random to a deli. The interarrival times are exponentially distributed with an average of 5 minutes. The deli prepares one order at a time. The order preparation times are exponentially distributed with an average of 3 minutes. 13. What kind of waiting line model is appropriate for the deli? 14. What is the utilization? 15. What is the total amount of time a customer would expect to spend at the deli (from walking in...
Single Channel, Poisson Arrival, and Exponential Service Time (M/M/1)Arrival rate ? 4Service rate µ 5Average Number of customers waiting for service Lq 3.2000Average Number of customers in the system (waiting or being served) L 4.0000Average time customers wait in line Wq 0.8000Average time customers spend in the system W 1.0000System utilization ? 0.8000Service time 1/µ 0.2000Probability of zero units in system P0 0.2000n 3Probability of 3 units in system P3 0.1024?????????People call a suburban hospital’s health hotline at the rate...
At a hair salon served by only one hairdresser, customers arrive at the rate of about 8 per hour according to a Poisson distribution. It takes about 5 minutes for the hair dresser to complete each customer, following an exponential distribution. What is the average time (in hours)the customer has to wait in the salon?
Customers arrive at Paul Harrold¡¯s styling shop at a rate of 3 per hour, distributed in a Poisson fashion. Paul a perform haircuts at a rate of 5 per hour, distributed exponentially. a) Find the average number of customers waiting for haircuts.b) Find the average number of customers in the shopc) Find the average time a customer waits until it is his or her turn.d) Find the average time a customer spends in the shope) Find the percentage of time...
Customers arrive at bank according to a Poisson process with rate 20 customers per hour. The bank lobby has enough space for 10 customers. When the lobby is full, an arriving customers goes to another branch and is lost. The bank manager assigns one teller to customer service as long as the number of customers in the lobby is 3 or less. She assigns two tellers if the number is more than 3 but less than 8. Otherwise she assigns...
7.4 During lunch hour, customers arrive at a fast-food restaurant at the rate of T20 customers per hour. The restaurant has one line, with three workers taking food orders at independent service stations. Each worker takes an exponentially dis- tributed amount of time-on average 1 minute-to service a customer. Let X, denote the number of customers in the restaurant (in line and being serviced) at time t. The process (Xt)PO Is a continuous-time Markov chain. Exhibit the generator matrix
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Customers arrive at the coffee shop in Bilkent FBA atrium, with a mean rate of 80 per hour (assume Poisson). It takes the barista, on average 30 seconds per cup of coffee (assume Exponential). Assume also that each customer buys only one cup. Determine: (a) The average number of customers waiting in line. (b) The average time customers spend in the system. (c) The average number of customers in the system. (d) The probability that a customer will not have...
Customers arrive at Lisa’s Hair Salon during a day in any particular business hour according to a Poisson distribution with a rate of ? = 3 per hour. Now the salon has two barbers who can each service a customer in exactly 30 minutes. Suppose a customer, Amy, arrives at 2:00pm and finds both barbers idle. (a) What is the probability that we will observe customers waiting before 2:30pm? (b) What is the probability that Amy observes the next customer...
A shop has an average of five customers per hour 5. A shop has an average of five customers per hour (a) Assume that the time T between any two customers' arrivals is an exponential random variable. (b) Assume that the number of customers who arrive during a given time period is Poisson. What (c) Let Y, be exponential random variables modeling the time between the ith and i+1st c What is the probability that no customer arrives in the...