Suppose that the number of spam emails that arrive to your Google account follows a Poisson process with a rate of AG = 2 per hour, the numb of spam emails that arrive to your AOL account follows a Poisson process with a rate of =1 per hour, and the two Poisson processes are independent

Suppose we have a small call center staffed by two operators A and B handling three telephone lines. A only handles line 1, and B only handles only line 2 and 3. Calls arrive according to a Poisson process with rate A = 100 calls per hour. All arrivals prefer line 1. Arrivals find all lines are busy will go away. Service times are exponentially distributed with a mean of 4 minutes. Customers are willing to wait an exponentially distributed length of time with a mean of 8 minutes before reneging if service has not begun. Describe a continuous time Markov chain to model the system and give the rate transition diagram and the generator G.

Consider two types of call arrivals to a cell in a mobile telephone network: new calls that originate in a cell and calls that are handed over from neighboring cells. It is desirable to give preference to handover calls over new calls. For this reason, some of the channels in the cell are reserved for handover calls, while the rest of the channels are available to both types of calls. = = Suppose that all calls arrive in a cell according to a Poisson process with rate Anc 125 calls per hour for new calls, and λho 50 calls per hour for handover calls. The cell has a capacity of 10 channels. Each call occupies 1 channel and the call time has an exponential distribution with mean two minutes. Suppose that no channels are reserved for handover calls. (a) Calculate the blocking probability in the cell and find the average number of channels used. (b) When a call has to wait, find its average waiting time.

Please answer the 3 questions

A small bank has two tellers, one for deposis and one for withdrawals. The service time for each teller is exponentially distributed, with a mean of 1 min. Customers arriving at the bank according to a poisson process, with mean rate 40 per hour; it is assumed that depositors and withdrawers constitute separate poisson processes, each with mean rate 20 per hour , and that no customer is both a depositor and a withdrawer. The bank is thinking of changing the current arrangement to allow each teller to handle both deposits and withdrawals. The bank would expect that each teller's mean service time would increase to 1.2 min, but it hopes that the new arrangement would prevent long lines in front of one teller while the other teller is idle, a situation that occurs from time to time under the current setup. Analyze the two arrangements with respect to the average idle time of teller and the expected number of customers in the bank at any given time.

A bank has established two counters, one for commercial banking and the second for personal banking. Arrival and service rates at the commercial counter are 6 and 12, respectively. The corresponding numbers at the personal banking counter are respectively 12 and 24. Assume that arrivals occur in Poisson processes and service times are exponentially distributed. (5.2) What is the effect of operating the two queues as a two server queue with arrival rate 18 per hour. What conclusion can you draw from this operation?

The process for cleaning up waste in a nuclear reactor core room eliminates 85% of the waste present in the area. If there is 1.7 kg of waste in the room at the beginning of the monitoring period and 2 kg of additionalwaste are generated each week, determine a recurrence relation and initial conditions describing the amount wn, of waste in the core room at the end of week n of the monitoring period.

A pump operates 1000 hours/year. Under a minimal repair concept, the pump failures generated a non-homogenous Poisson process having the following intensity function with t measured in operating hours. Row(t)=0.00003t^2. a) From the information given, is the rate of occurance of failure (ROCOF) increasing, decreasing or remaining constant? b) Calculate the number of expected failures of the pump over 1000 hours of operation. c) Calculate the MTBF for the 1000-hour operation. d) The repair time of the pump is best described by the following probability density function h(t)=t^2/3 for 0<_t<_3 hours. WHat is the mean time of repair, in hours? e)What is the inherent availability of the pump over the 1000 hours?

A Toy manufacturer has noticed that the number of faulty Toys detected in a production depends on the supervisor on duty and is detected according to a Poisson Process. There are only 2 supervisors: A and B, in the firm. The average number of faulty Toys is 3 per day when A is on duty, while the average number of faulty Toys is 4 per day when B is on duty. quality of one day's production does not have an effect on the next day. B works 4 out of 5 days, while A works 3 out of 5 days.   a) What is the probability that no faulty Toys will be produced tomorrow, if B is on duty? b) What is the probability that no faulty Toys will be produced in the next two days? c)  Suppose at least one faulty Toy was produced yesterday, what is the probability that A was on duty?

4