### Table 4. Queue length distribution (for djpeg) # occupied

2002

"... In PAGE 8: ... We found that for any bench- mark, more than 96% of the messages do not have to wait because they find the queue empty, and the maximum num- ber of occupied entries was 9. For instance, Table4 shows a typical queue length distribution (for benchmark djpeg). Although 9-entry queues are long enough in our exper- iments, the model should ensure that data is never lost, to guarantee execution correctness.... ..."

Cited by 27

### Table 3: 0:999 quantile of queue length distribution for utilization, u = 0:9:

1995

Cited by 45

### Table 5: Stationary queue length distribution for the binomial case, n = 16, q =0.5, s = 10.

in Manuscript:

2005

"... In PAGE 18: ...5, s = 10. Table5 displays some of the xj, calculated by xj(L)forL =10, 20, 30. Additionally, the xj have been determined from (12) where the roots of zs = A(z) outside the unit circle follow from (25) (with the sum over l truncated at l = 60).... ..."

### Table 5: Stationary queue length distribution for the binomial case, n = 16, q = 0:5, s = 10.

2004

"... In PAGE 21: ...xample 5.8. Consider the binomial case, A(z) = (p + qz)n where p, q 0, p + q = 1, for which we take n = 16, q = 0:5, s = 10. Table5 displays some of the xj, calculated by xj(L) for L = 10; 20; 30. Additionally, the xj have been determined from (12) where the roots of zs = A(z) outside the unit circle follow from (25) (with the sum over l truncated at l = 60).... ..."

### Table 4: Stationary queue length distribution for A(z)=Y (z)6, with Y (z) given in (57), s = 30.

in Manuscript:

2005

"... In PAGE 18: ... For (23), (25) and (51) we truncate the sum over l at l = 60. The results are displayed in Table4 . We see that both Table 4: Stationary queue length distribution for A(z)=Y (z)6, with Y (z) given in (57), s = 30.... ..."

### Table 4: Stationary queue length distribution for A(z) = Y (z)6, with Y (z) given in (83), s = 30.

2004

"... In PAGE 21: ...results are displayed in Table4 . We see that both (12) and (50) lead to similar results as obtained in [10].... ..."

### Table 2 : E ect of Tra c Burstiness on Performance Measures The burstiness of the source increases with M causing the log-tail of the queue length distribution to be attened. Except for the values of PrfL ng with n near 0, the curves with di erent M-values are linear on a logarithm scale with slopes whose magnitudes decrease with M.

"... In PAGE 9: ...M 1 2 4 8 S = 1 106 143 274 626 S = 2 106 143 274 627 S = 4 106 143 275 628 S = 8 107 145 278 633 Table 1 : Bu er Requirements to Achieve CLP lt; 10?9 Figure 3 illustrates the e ect of bursty tra c on the tail distribution of the entry monitor with parameters (R; T; S) = (66; 600; 4). Table2 contains i) descriptors of the arrival process - expectation, variance, squared coe cient of variation (CV 2) and ii) performance measures of the monitor - expectation and variance of the queue length, - the size of the bu er N(10?9) required to achieve a cell-loss probability 10?9, and - the root # of 0 = zR ? PT (z) outside of the unit disk of smallest modulus. 16 32 48 64 80 0.... ..."

### Table 1: Comparison of average queue lengths (in packets) predicted by different queue models

2003

"... In PAGE 6: ... Looking only at the queue length distribution, the im- provements achieved with our more sophisticated queue mod- els may appear to be marginal, but if we look at the average queue length, which is surely an important metric, we see that the MS[X]/M/1 model and even more the MS[X]/E10/1 model provide results much better than the M[X]/M/1 model. A comparison of results for the average queue length is re- ported in Table1 for four different values of link utilization. The sim column contains average values and 95% confi- dence intervals obtained by simulations.... ..."

Cited by 10

### TABLE IV VARIANCE OF QUEUE LENGTH FOR THE DIFFERENT SIMULATION RUNS FOR CASES WHERE PROPAGATION DELAYS HAVE UNIFORM, EXPONENTIAL AND PARETO DISTRIBUTIONS Run Number Uniform Exponential Pareto

2004

Cited by 3

### Table 4 Average queue lengths and waiting times

"... In PAGE 13: ... These parameter values apply to results shown in Tables 3 through 6. Estimates of expected values obtained by simulating several quanti- ties of interest in connection with queuing delays in the model are given in Table4 . These quantities-average waiting time in the DTU DTU busy idle TDTU(c) loo-TDTU(c) 46.... In PAGE 14: ... Using this notation, we define average CPU and DTU queue lengths as the following random variables: k li(ti,l - ti) i=l LCPU(C) = and tk+ 1 k apos; W+l - 0 LDTU(C) = f= apos; tk+ 1 Here, tk+l is the epoch at which the c + 1st customer begins his a1 service, and t:+l is the epoch at which the c + 1st customer begins his p1 service. Table4 gives estimates of the expected values of the four quantities just defined as a function of c and the rate parameter X, of the exponentially distributed cy2 service time. Again, the other parameter values have been defined earlier in this paper.... ..."