CSCI 8710
Homework #2

Assigned: Tuesday, Sept. 9th

Due: Tuesday, Sept. 23rd, in class

All problems are in "Performance by Design" by Menasce, Almeida, and Dowdy

Ch. 3, exercises 1, 3-7, 10

The solutions:

Ch.3, Ex. 1 -


N = average multi-programming level = 5


      7200 transactions     1 hour       1 min       2 trans
X_0 =------------------ x  --------- x  -------- =  ---------- 
          hours              60 min      60 sec        sec

Applying Little's Law:

	N = X_0 * R

	     2 trans
        5 =  -------  * R
               sec

	R = 2.5 sec

Ch.3, Ex. 3 -


		Throughput vs. N

        |
     20 |                 * <- max at light load = 6.711 * N
        | ********************************* max at heavy load = 17 t/s
     16 |
        |           *
     12 |
        |
      8 |			Observation: throughput max's out just below
        |     *			average of 3 concurrent jobs
      4 |  
        | 
        -------------------------------------------
        0     1     2     3     4
			N

Ch.3, Ex. 4 -

	 5400 trans 	 1 min 		    3 trans
	 ----------- x  --------------  =   --------
	  30 min	 60 sec               sec


	 18,900 ops 	1 min 		    11 ops
	 ----------- x  --------------  =   --------
	  30 min	60 sec               sec


	   11 ops 	1 sec 		    3.67  ops
	 ----------- x  --------------  =   --------
	   sec 		 3 trans             trans

	  0.40 busy-sec     1 total-sec         0.1333 busy-sec
	 -------------- x  --------------  =   --------------- = D_disk
	   total-sec          3 trans             trans

#5:


  5400 t         1 hr         1 min           1.5 t
----------  * ----------- * -----------  =  ---------
   hr           60 min        60 s              s


   	     0.030 s 
  S_disk =   -------
             visit

	    3 visits
  V_disk = ----------
             trans 
            

           0.030 bs       3 visits       0.09 bs
D_disk =   ----------  * ----------- * -----------  
            visit           t               t



           0.09 bs        1.5 t          0.135 bs      
U_disk =   ----------  * ----------- = -----------  = 13.5%
             t             ts               ts

#6:



  packet delay = 100 msec = 0.100s

  throughput = 128 packets/s

  N = R * X_0


                   128 packets    
  N =  0.100s  *   -----------  = 12.8 packets in transit
                       s

#7:

    7200 req     1 min      2 req
    -------- *  -------  = --------
     60 min      60 s         2


                     0.30 bs
   U_disk = 0.30 =   -------
                       ts


    V_disk = ??


               0.30 bs        1 ts        0.15 bs
    D_disk =  ---------  *  --------  =  ----------
                ts            2 req        req 


    D_disk = S_disk * V_disk

     0.15 bs       0.030 s        5 i/o s
    ---------  =  --------   *   ----------
       req           i/o            req


               5 i/os
     V_disk = --------
                req

#10:

	M = 50 terminals
	Z = 5 s 
	U_disk = 0.60
	S_disk = 0.030 s
	V_disk = 4

	Response time?

		  0.030 s     4 i/o 	  0.120 s
	D_disk = -------- *  --------- = --------- 
                   i/o         req          req


		 1 req      0.60 bs          5 req
	X_0 =  --------  * -----------  = ------------ 
                0.120 bs       1 ts           ts

              M
        R = -------  - Z
              X_0      

              50
          = -------  - 5
              5      


	  = 5 sec

Last modified: Tues Sept 30 2008

CSCI 8710 Homework #2

Assigned: Tuesday, Sept. 9th

Due: Tuesday, Sept. 23rd, in class

The solutions:

CSCI 8710
Homework #2