### Table 1: Average Risk of Classical Bootstrap and Proposed Bayesian Estimators for Average Sojourn Time in a Single Server Queue

"... In PAGE 8: ... ={z1, z2,...,zn} is the observed sample of service times. Table1 shows the results for the average risk in es- timating the posterior mean response. It appears that the Bayesian point estimator averages a slightly smaller risk in all cases.... ..."

### Table 1 Phase-type distributions of the sojourn time in the levels for the system new Level Representation Order

2005

"... In PAGE 14: ...25, that is, after each repair the mean lifetime of the system decreases at 20% of the previous mean lifetime. In Table1 we define the phase-type distributions for the four degrading levels when the system is new and has not completed any internal repair. The system also undergoes external failures, that arrive to the four levels with rates given by k1 = 0.... ..."

### Table 5: Simulation estimates and approximations for the mean sojourn time at station 2 for case 2 of ve systems

"... In PAGE 23: ... The superposition of these two arrival processes is the exogenous arrival process to station 2, which has asymptotic rate 1 + 3=2 = 2 and asymptotic variance 1c2 s;1 + ( 3=2)(1 + c2 s;3)=2. Therefore, ^ W SBD 2 = 2 2 1 ? 2 1 2 c2 s;2 + 1 2 c2 s;1 + 3 2 2 1 + c2 s;3 2 !! = 3 4 27 13 1 2 c2 s;2 + 3 4c2 s;1 + 1 4 1 + c2 s;3 2 !! : Table5 compares SBD estimates of mean sojourn time at station 2 for case 2 of the ve systems with simulation estimates, as well as QNA and QNET estimates. For subnetwork S1, station 2 is an instantaneous switch, and the resulting two station network is a generalized Jackson network as pictured in Figure 2, which can be analyzed via QNET.... ..."

### Table 2 gives the simulation estimates and approximations of the total mean sojourn time (calculated from formula (1.5)) in the network. Table 3 gives the mean sojourn time (service

"... In PAGE 19: ... A random variable is said to have hyper-exponential distribution with balanced means (having mean m and SCV c2 gt; 1) if it has density function f(t) = p 1e? 1t + (1 ? p) 2e? 2t; t 0; where p = 1 2 + 12 p(c2 ? 1)=(c2 + 1) and 1 = 2p=m and 2 = 2(1 ? p)=m. The simulations Sys=Case Sim QNA QNET SBD (n = 5) (n = 5) A 1 40:390 (3:75%) 20:519 (?49:20%) ( ) 42:986 (6:43%) 2 59:580 (3:29%) 36:039 (?39:51%) 56:679 (?4:87%) 58:175 (?2:36%) 3 40:720 (4:78%) 23:985 (?41:10%) 38:682 (?5:00%) 40:188 (?1:31%) 4 42:119 (3:36%) 26:221 (?37:75%) 41:808 (?0:74%) 42:655 (1:27%) B 1 52:399 (2:64%) 42:020 (?19:81%) 52:613 (0:41%) 50:200 (?4:20%) 2 91:523 (3:77%) 94:050 (2:76%) 83:704 (?8:54%) 95:270 (4:09%) 3 61:680 (3:44%) 72:230 (17:10%) 61:941 (0:42%) 60:902 (?1:26%) 4 63:336 (2:83%) 75:821 (19:71%) 64:142 (1:27%) 64:691 (2:14%) C 1 44:244 (1:96%) 31:298 (?29:26%) 37:031 (?16:30%) 47:092 (6:44%) 2 92:417 (4:23%) 87:443 (?5:38%) 91:169 (?1:35%) 91:648 (?0:83%) 3 44:263 (4:69%) 33:222 (?24:94%) 43:966 (?0:67%) 44:994 (1:65%) 4 50:202 (1:04%) 41:353 (?17:63%) 51:077 (1:74%) 52:227 (4:03%) D 1 55:813 (2:58%) 71:417 (27:96%) 58:754 (5:27%) 58:209 (4:29%) 2 98:364 (1:82%) 101:710 (3:40%) 97:198 (?1:19%) 94:363 (?4:07%) 3 47:718 (2:51%) 40:215 (?15:72%) 47:820 (0:21%) 48:206 (1:02%) 4 55:237 (4:37%) 49:281 (?10:78%) 55:990 (1:36%) 56:739 (2:72%) E 1 134:426 (4:77%) 265:110 (97:22%) 155:080 (15:36%) 115:694 (?13:93%) 2 213:101 (3:47%) 308:440 (44:74%) 228:248 (7:11%) 206:114 (?3:28%) 3 138:722 (3:97%) 243:750 (75:71%) 161:290 (16:27%) 135:280 (?2:48%) 4 155:054 (4:37%) 252:330 (62:74%) 167:831 (8:24%) 147:299 (?5:00%) Average absolute 32:12% 5:07% 3:64% percentage error Table2 : Simulation estimates and approximations for the total mean sojourn time of the three station network... In PAGE 20: ... The next paragraph gives a detailed discussion on how we partitioned the network into subnetworks when using the SBD method for this particular network. From Table2 it is evident that both QNET and SBD outperform QNA, with SBD slightly better than QNET in general. For case 1 of system A, the current implementation of the QNET algorithm fails to converge to a positive number.... ..."

### Table 2. Acuracy of Asymptotic Expansion

"... In PAGE 3: ... An analysis of this set of candidate solutions folows. For comparison, Table2 presents the eror values asociated with the asymptotic expansion when caried to betwen 1 and 4 terms. Table 2.... ..."

### Table 1: Asymptotic Messaging Costs Player distribution

"... In PAGE 4: ... In general, all operations take at most loga- rithmic time in terms of the number of peers, while some only take constant time. Table1 summarizes these results. In the following discussion, n is the number of nodes in the N-Tree, p is the num-... ..."

### Table 3: Sojourn Times for Scenarios 1 and 2

"... In PAGE 4: ... Overall of course, both SAR and IR clearly indicate the higher interactivity of the weather scenario. Table3 presents the average sojourn times in the four states of the COSM (Section 2.1.... ..."

### Table 2: Mean sojourn times service organisation

"... In PAGE 7: ... Suppose we can hire six additional employees. Table2 shows the mean sojourn times of the organisation for allocations up to 17 employees. From this table, we deduce that the first employee to hire would be an operator (because 21.... ..."

### Table 3.5 : Mean remaining sojourn time and mean handover sojourn time.

### Table 1 Vanishing terms in the asymptotic expansions.

1996

"... In PAGE 4: ...n both cases. For the soft clamped plate 0, 1, and 2 all vanish. In all ve cases, the rst nonzero boundary corrector is purely tangential. Table1 summarizes the terms in the asymptotic expansions of ! and which vanish. Table 1 Vanishing terms in the asymptotic expansions.... ..."

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