Tietojenkäsittelytieteen laitos

Perf. Eval., Homework 5 (due 17.4.2002)

1. A long time ago one weekend Teemu went to buy gas. The Esso station had no lines but the price was 4.59 mk/l. On the other side of the street was a brand new Jet station which had about 20 cars in line before the pumps but the price was only 3.99 mk/l. There was no hurry, so the Jet station was chosen. While waiting in line he observed, that the line seemed to be about 20 cars all the time. The line could not grow much more because all but seven cars were waiting on the side of the street. There was only one single line to the four pumps that all seemed be occupied all the time. It took seven minutes from him to move 10 positions forward in line.

   Describe this system in terms of queueing network models.
   (What type of system? Queueing network? Job classes? Population? Arrival rate? Service time? Departure rate? Response time? Time in queue? Device utilization? Queue lengths?)
   Describe the results in terms better suitable for an average service station customer.
   How many pumps would have been needed that Teemu would have got his gas (queueing time included) in 5 minutes?
   What are your conclusions?
    

2. Solve the multiple class open model file server example (slide 8 in lecture notes, Table 6.8 [Men 84]) with Menasce's Excel workbook for open model. These workbooks are available in the Web and to modify them you need a password that is given in Menasce's book published in 2001. Get the solutions for the original model and for the same four modifications as given in class.
     
3. [2 HWP] Consider a time-sharing system with one cpu and a disk. Workload consists of interactive and batch jobs. Interactive jobs from 25 terminals require in average 10 page swaps from the disk, each of them followed by a short burst of CPU averaging 10 msec. Batch jobs require one disk swap followed by uniterrupted CPU execution of 1 second in average. The multiprogramming level for batch jobs is set to 10. Thinking time at terminals is 30 seconds in average. Page and disk swaps take 90 msec in average. Disk rotation speed is 3600 rpm.

   It is assumed that the batch work load will increase, requiring at least batch throughput of 4.5 jobs per second. It is anticipated that a CPU 5 times as fast as current would be sufficient.

   Build a model for this system, estimate the parameters and solve the model with some solution package (Menasce's workbook, PMVA, your own?).

   1. What are the system throughput and response times (in each job class) in the original system?
   2. What are the system throughput and response times (in each job class) in the proposed system?
   3. Is there anything peculiar in the new system performance? What? Why?
   Please bring to practice session listings of your model, inputs and outputs. Bring also the input files in diskettes or have them available at the file server so that you can demonstrate your model.
      
4. [2 htp] Read article Chandy & Neuse, Linearizer: A Heuristic Algorithm for Queueing Network Models of Computer Systems, Comm ACM 25, 2 (Feb 1982), p. 126-134.
   1. How does linearizer differ from Approximate MVA given in class?
   2. Why would linearizer be better? Can it be worse?
   3. Try linearizer solution for the the network given in problem 5 in homework 4. (PMVA has built-in linearizer solution method LIN). Compare that solution to the exact solution as well as to the solution given by the Bard-Schweitzer Approximate MVA given in class (PMVA solution method SCHWEITZER ).
   4. Which approximation does Menasce use in his Excel workbooks for closed models? (Try it out, and check which PMVA solution matches Menasce's solution.)

   A copy of the article can be found in the library or in the course folder in room A412.