# Errata for "Performance Modeling and Design of Computer Systems"

• p. 24 For Open Systems, provided that the system is not in overload, the throughput, X, is defined by the arrival rate into the system. As such, X is not affected by increasing the \mu_i's.
• p. 24 Throughput and response time are *not necessarily* related. For example, you might decrease response time, by increasing \mu, without ever changing the throughput. You might also decrease response time by changing the scheduling policy, without ever changing the throughput.
• p. 36. Bayes Law and Extended Bayes Law should both include the words: Assuming P{E}> 0.
• p. 43. Replace f(y) with f_X(y)
• p. 47. In the expression for \var(X), the term involving an integral should use little x not big X.
• p. 49. Def 3.21. Replace "Let A be an event" with "Let A be an event s.t. P{A} > 0."
• p. 61. Thm 3.33 Replace "variance" by "finite variance."
• p. 65. Exercise 3.4. Replace "each with positive probability" with "each with positive probability and with non-zero intersection."
• p. 65. Exercise 3.8(a). Replace "Which has lower variance" with "Which is lower?"
• p. 76. "For the previous examle we could have used the Inverse-Transform method." This is not true. While it is easy to get the c.d.f., it is not easy to invert it.
• p. 97. Recall from Chapter 2 that, for an open system, throughput and mean response time are not necessarily correlated. By contrast, Little's Law tells us that, for a closed system, they are always inversely correlated.
• p. 105. 2nd line: 0.775 * 40 should be 0.0775 * 40.
• p. 112. Exercise 6.3. Edit to say: David explains that 10% of jobs end up going to the database, where their mean response time is 10 seconds. The remaining 90% of jobs don't need to go to the database and thus have a mean response time of only 1 second.
• p. 119. In the text, N = 20 should be replaced with N=10, so that it matched the figure.
• p. 120. Remove the entire line: T=650 seconds (the length of the observation interval).
• p. 124. Exercise 7.4. Remove the entire line: "Observation interval = 17 minutes."
• p. 143. The following sentence is missing: "Specifically, a packet can "arrive" and "depart" within the same time step, leaving the system in the same state." This sentence should be placed just after the sentence: "Note that during a time step, we might have both an arrival and a transmission, or neither."
• p. 152. non-negative coefficients --> non-negative integer coefficients
• p. 153. The \vec{e} in the first displayed math line shouldn't be there.
• p. 184. Exercise 9.4. "n>1 states" should be "at least one state", so that it's clear that the chain may be infinite.
• p. 185. Exercise 9.8. The graph needs to be connected with w_{ij} = w_{ji} \geq 0, forall i,j.
• p. 187. Exercise 9.12. In the definition of stopping time, the event {N=n} is independent of X_{n+1}, X_{n+2}, ... GIVEN the values we've seen, namely, X_1, X_2, ..., X_n.
• p. 222. Exercise 11.4. The density function is defined for t \geq 0.
• p. 358. Exercise 20.2 -- Taile => Tailed
• p. 361. In Figure 21.2, the p and 1-p probabilities are interchanged.
• p. 398. For the M/E_k/1 queue, the fomula hold if k is odd. If k is even, then the formula shown should not have a ceiling.
• p. 436-437. In taking the nth derivative, must write ds^n. Likewise for kth derivative ds^k, and for 2nd derivative ds^2.
• p. 446. Exercise 25.6. Assume that the Poisson process has rate \lambda.
• p. 446. Exercise 25.7. X is non-negative and continuous.
• p. 492. The final equality in the expression of E[S^n_{\bar{x}}] is missing an "n".
• p. 501. The formula for E[S_e] should be E[S^2]/(2 E[S]).
• p. 517. The line with the (why??) should have \mu_i rather than \mu
• p. 525. Figure 33.2. The x-axis should be labeled 0, 2, 4, 6, 8, 10. The decimals shown there are wrong.

Please send me more errors as you find them: harchol@cs.cmu.edu