Question

(b) There ane 45 clientscnaLAN with a single database server. Each client issues a request every 10 secoeds on an average to the database server. The server processes the request i approximately 0.5 seconds Clients requests are assumed to fellow the Poisson distribution and server's processing time follows exponential distribution. What is the system utilization? )How long does an average request take on the server (waiting if any and processing What is the average number of requests waiting to be peocessed? Page S of

Answer 1

(b) The client's requests are assumed to follow Poisson distribution with mean 10 seconds so λ = 0.1 per seconds and server's processing time follows exponential distribution with mean 0.5 seconds so μ 2 per seconds (i)The system utilization is given by 10 0.5 λ0.1 ρ=-=-=0.05 (ii) To find how long average request take on the server W, we need to calculate average number of client requests in the queue Lo L = 0.05 ー 0.0026 1-p 1-0.05 Wait time in the Queue Wa 0:0020.0263 seconds 0.1 average request takes on the server WW W-L +0.0263+0.5263 seconds