Alcuni altri esercizi svolti

Pagina 1

1. A coffee company requires its clients to first get a ticket with a progressive number, then numbers are called by one of three free counters, and finally costumers are offered a free coffee. We imagine that the three counters operators are all with identical service speed, and that only one customers out of two accept the free coffee, which is served by another single operator. The ticket machine can provide 12 tickets per minute, the mean service time for a costumer is 2 minutes, and the time required to prepare the free coffee is 30 seconds. (a) Draw a visual representation of the system. (b) Compute the visits and the demands of all the service centers. (c) Identify the bottleneck. (d) Which is the maximum number of costumers per minutes that the system is able to serve? (e) How many operators at counters and at the free coffee point should be present to make the ticket machine the bottleneck? (f) If costumers arrive at a rate of 1 per minute, the mean service time is 3 minutes at the counters. Which is the mean number of costumers in the shop in this case? SOLUTIONS: (a) (b) Dticket = 1 Xticket ; Dcounter = 1 3120 = 40sec; Df ree = 1 230 = 15sec (c) Bottleneck is counter (d) Xmax = 1 Dmax = 1 40 = 0.025rec/sec = 1.5req/min (e) Bisogna far scendere la D di ogni stazione sotto laDticket, aumentando il numero di stazioni. 6 counter e 4 free. (f) N = XR con R somma dei tempi delle singole stazioni. Xmax = 1 60 = 0.01666; R = 60 + 60 + 15 = 135; N = 2.25 2 3. A storage server, has two power supply units (PSU), two network adapters, and four disks in RAID 1+0 (two groups of two disks each). The parameters of the compo- nents are the following: M T T FP SU = 998 days, M T T RP SU = 2 days, M T T Fnet = 4995 days, M T T Rnet = 5 days, M T T Fdisk = 990 days, M T T Rdisk = 10…