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

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.

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?

Emails arrive according to Poisson process with mean 34/h.What is the sd of the arrival time of the 5th email, given that the third email has not arrived yet after 2 minutes, but the second email has?

A car servicing station has 2 bays where service can be offered simultaneously. Because of space limitation, only 4 cars are accepted for servicing. The arrival pattern is Poisson with 12 cars per day. The service time in both the bays is exponentially distributed with µ = 8 cars per day per bay. Find the average number of cars in the service station, the average number of cars waiting for service and the average time a car spends in the system.

Suppose that the number of customers arriving to a store follows the Poisson process with rate 1/λ per minute. Choose an option that is not correct.  The expected number of customers arriving to the store between 9am and 11am is twice bigger than the expected number of customers arriving to the store between 10am and 11am. The number of customers arriving to the store between 9am and 10am is independent of the number of customers arriving to the store between 10am and 11am. The expected number of customers arriving to the store between 9am and 10am is 60λ. The number of customers arriving to the store between 9am and 10am follows the same distribution as the number of customers arriving to the store between 10am and 11am

~if calls to your cell phone are a Poisson process with a constant rate lambda=2 calls per hour, what's the probability that, if you forget to turn your phone off in a 1.5 hour movie, your phone rings during that time? ~How many phone calls do you expect to get during the movie?

A large automotive repair shop has instituted a system for mechanics to check out the needed supplies from the Parts Department. Observation of the system has shown that the rate of arrivals of mechanics (who are internal customers in this setting) to check out supplies follows a Poisson distribution with an average rate of 10 per hour. It takes an average of 5 minutes to get the supplies to the mechanic and these times follow an exponential distribution. Assume that there is currently only one person working at the service window in the parts department. The hourly salary of the service attendant (resource unit) is 30$ and the hourly salary of the mechanic is $40. What is the total system time cost? 30$ 200$ O 20$ 240$ 50$

Suppose a researcher is interested in determining how friends and family arrive to parties. | The researcher attends a party where the host invites 26 friends and 17 family members and records whether each person arrived early (more than 5 minutes before the time given on the invitation), on-time (between 5 minutes before and 5 minutes after the time given on the invitation), or late (more than 5 minutes after the time given on the invitation). Suppose the researcher obtained the following data shown in the contingency table below. Early On-time Late 11 Friend Family Member 5 10 10 5 2 6. State the null hypothesis and alternative hypothesis for this investigation in complete sentences. 7. Copy the observed values provided here into the table on your template. Find the expected counts for each cell and write them next to the observed values. (Make sure to clearly label the observed and expected counts. Make sure to show your work in the space provided for this question as well.) 8. Find…

Suppose that the link speed is 8 Mbps, the demand bandwidth of each active user is 1000Kbps. The active probability of each user is 10%. How much user can support under the block probability is less than 0.008?