A hexagonal cell within a seven-cell system has a radius of 1.52 km. A total of 140 channels are used within the entire system. If the load per user is 0.028 Erlangs, and 1 = 2 call/hour, compute the following for an Erlang C system that has an 8% probability of delayed call: a) How many users per square kilometer will this system support? b) What is the probability that a delayed call will have to wait for more than 9 sec?
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- Assume that a network Access Multiplexer has to multiplex 10 subscribers connected at c bps and subscriber is active 1/3 of the time. Show by means of calculations what the minimum over-subscription ratio should be to make the overflow probability less than 1%.Consider the following tele-traffic scenario faced by the Nizwa Firq Telephone Exchange. On a particular day from 6am to 6.15am, the exchange handles 8 calls of average call duration 1 mins. The number of calls and the average call duration both doubles (from its values in previous time slot) every 15 mins untill 7am. Calculate the total traffic handled by the telephone exchange for the time duration 6am to 7am.A local café has a single cash register, with a single assistant to work it, and three serversworking to fill the customer orders. Customers arrive with exponential interarrivaltime an average of one every 2 minutes. The time to place their order and pay at theregister is normally distributed with mean 90 seconds and standard deviation 20 seconds.Each customer’s order is then passed to one of the servers who take on average5 minutes with standard deviation 1.5 minutes, also normally distributed, to fill the order.a. Calculate the capacity of the register and the servers. What is the bottleneck inthis system?b. Calculate the average utilizations of the register and the serversc. What is the probability a customer is delayed at the register?d. What is the expected time from a customer’s arrival to the order being passed on tothe servers (including any queueing time)?e. Estimate the probability that there is a delay between a customer placing his orderand a server beginning to work on the…
- A local café has a single cash register, with a single assistant to work it, and three servers working to fill the customer orders. Customers arrive with exponential interarrivaltime an average of one every 2 minutes. The time to place their order and pay at theregister is normally distributed with mean 90 seconds and standard deviation 20 seconds. Each customer’s order is then passed to one of the servers who take on average5 minutes with standard deviation 1.5 minutes, also normally distributed, to fill the order.g. Estimate the expected time from the servers receiving an order to it being ready forthe customer (including any queueing time).A local café has a single cash register, with a single assistant to work it, and three servers working to fill the customer orders. Customers arrive with exponential interarrival time an average of one every 2 minutes. The time to place their order and pay at the register is normally distributed with mean 90 seconds and standard deviation 20 seconds. Each customer’s order is then passed to one of the servers who take on average 5 minutes with standard deviation 1.5 minutes, also normally distributed, to fill the order. a.) Calculate the capacity of the register and the servers. What is the bottleneck in this system? b.) Calculate the average utilizations of the register and the servers c.) What is the probability a customer is delayed at the register? d.) What is the expected time from a customer’s arrival to the order being passed on to the servers (including any queueing time)? e.) Estimate the probability that there is a delay between a customer placing his order and a server…A local café has a single cash register, with a single assistant to work it, and three servers working to fill the customer orders. Customers arrive with exponential interarrival time an average of one every 2 minutes. The time to place their order and pay at the register is normally distributed with mean 90 seconds and standard deviation 20 seconds. Each customer’s order is then passed to one of the servers who take on average 5 minutes with standard deviation 1.5 minutes, also normally distributed, to fill the order. a.) Calculate the capacity of the register and the servers. What is the bottleneck in this system? b.) Calculate the average utilizations of the register and the servers c.) What is the probability a customer is delayed at the register?
- Let there are 7680 cross points in a switch. If the number of crosspoints is to be reduced by the factor of 3 with non blocking what is the probability that a call will be blocked ? Assume the utilization probability p = 15%.In a cellular network, each cell has seven channels, two of which are dedicated solely for handoff calls. Assume that both new and handoff call arrivals are subject to a Poisson process. The average arrival rate of new calls and handoff calls is 1.5 and 0.3 calls per minute, respectively. The holding duration of a channel is exponentially distributed, with a mean of 2 minutes. Determine the blocking probability of new and handoff calls.Consider a web-server that receives web requests at an average rate ? of 20 requestsper second that follows a Poisson distribution. Answer the following questions:(a) What's the probability that it would receive 1000 requests in a minute? (b) What's the probability that no requests will arrive for 3 seconds? (c) Consider one second and assume that 20 requests already arrived in 0.5 second, whatis the probability that 20 requests will arrive in the next 0.5 seconds? (d) If you found out that the web-server was 70% of the time busy on average, what wouldbe its average service rate?
- In Example 13.4 of section 13.5, we examined whether an M/M/1 system with a single fast server is better or worse than an MMs system with several slow servers. Keeping the same inputs as in the example, use simulation to see whether you obtain the same type of results as with the analytical models. Then repeat, using gamma-distributed service times with standard deviation six minutes. Example 13.4 COMPARING ONE FAST SERVER TO SEVERAL SLOW SERVERS Which system has the better steady-state characteristics such as L, W, LQ, and WQ: a single-server system where the single server can serve 30 customers per hour or a five-server system where each of the servers can serve six customers per hour? For each system, we assume that customers arrive according to a Poisson process at rate 25 per hour. Objective To see whether customers should prefer a system with one fast server or a system with several slower servers. Example 13.5 INCREASINGLY LONG LINES AT COUNTY BANK Over a period of time,…Computer Science find the blocking probability (Pb)for different number of subscribers N ( 20,40,60,80) and plot the Pb vs N. for given N, what is the maximum user activity to satisfy a blocking probability of 0.001, plot user activity vs N..In order to function optimally, what are the three conditions that must be true for each given network? Spend a minute or so explaining what one is like in your own words.