### Table II. { Various time scales in the route to stochastic behavior.

### Table I. { Various time scales in the route to stochastic behavior.

### Table 1: Performance comparison of the queuing with the Nagel-Schreckenberg model for Wup- pertal and NRW. It is a naturally arising question whether this algorithm for the route choice will converge. Due to the stochasticity of the underlying route choice model only a stochastic equilibrium, where the 4

2001

"... In PAGE 4: ... Due to its intrinsic properties the queuing model is the faster the longer the average link lengths in the network are. For example, applied to the network of Wuppertal (see Table1 ) with an average link length of 0.3 km it is faster by approximately one order of magnitude, but almost two orders of magnitude for the freeway network of the German Bundesland Nordrhein-Westfalen (NRW) with an average link length of 2.... ..."

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### Table 6: Results from the stochastic model/design/performance evaluation

2001

"... In PAGE 14: ... On the other hand, as we shall see in Section 5.5 and Table6 , the same design evaluated in the stochastic environment gives loss probabilities for certain streams as high as 0.137.... In PAGE 18: ... Hence, our goal is to obtain the smallest value of the compensation factor such that the di erences between the loss ratios and loss probabilities on service routes in the two approaches are all just within a user-speci ed error tolerance. Our results are presented in Table6 . A notable feature is that the video service class is uniformly the most adversely a ected in QoS.... ..."

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### Table 3: Route travel costs with the optimal toll Charge

"... In PAGE 9: ...4 Reliability Paradox Note that the route costs (sum of travel time and tolls) with a toll of 2.5 euros are not equal for all routes (see Table3 ). This does not violate the equilibrium principle as we use a logit-based stochastic assignment instead of a deterministic equilibrium.... ..."

### Table 3. Stochastic transition relation for stochastic CCP

2006

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### Table II: Stochastic Resonance versus Stochastic Chaos

### Table 4 lists the times spent in the XACT tool. Since the HDL compiler is not integrated into XACT, the first column lists the com- bined times for reading the mapped netlist and placement. The mapped netlists were produced with our Lola compiler and a con- version tool. With no hints, XACT uses more time in the placement phase, trying to produce a good placement using stochastic algo- rithms. Repetitive runs on the same input do not yield the same re- sult, which can affect the result of the routing phase as well. Hence, little progress can be made between iterations. The placement and the routing can be influenced by the user through various switches. To produce the data presented in Table 4, those settings were cho- sen that ran the fastest, or achieved a completed design.

1998

"... In PAGE 5: ... Table4 : Speed of XACT (Times in Seconds) Table 5 lists the total times and the speedup obtained by using the Lola system. As the table shows, the Lola system is one to two orders of magnitude faster than the commercial tool.... ..."

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### Table 2. Model stochasticity.

2006

"... In PAGE 3: ... The PLAN C model produces as its output the individual traces of all its agents and statistical infor- mation about the time-course of the global behavior. In this paper, we have decided to investigate and analyze the three criteria presented in Table2 : the percentage of fatal- ities, average ill-health of the affected5 population (at the end of 16 hours) and the average waiting time at the hos- pitals (during the first 16 hours). The global behavior is the emergent interaction between the different classes of agents and available resources for the specific emergency scenario.... In PAGE 4: ... It follows that one simulation is not enough to evaluate the fitness function, and can only be considered as an esti- mate of the fitness. In order to study the stochasticity of the PLAN C model, Table2 shows the error rate in the esti- mation of the different analyzed objectives with respect to a true fitness value estimated on 1000 independent runs. As expected, the stochasticity is different for each objective / criteria: the number of fatalities and the average waiting time are more sensitive to the stochastic behavior than the average ill-health.... ..."

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### Table 1. Stochastic automata for

1999

"... In PAGE 3: ...The set of edges ?! between locations is defined as the smallest relation satisfying the rules in Table1 . The func- tion F is defined by F(xG) = G for each clock x in p.... In PAGE 6: ... Since in our semantics (cf. Table1 ) a location corre- sponds to a term, simulation can be carried out on the ba- sis of expressions rather than using their semantic repre- sentation. This means that the stochastic automaton is not entirely generated a priori but only the parts that are re- quired to choose the next step.... In PAGE 6: ...erm pi (i.e. location) and the input specification E. From term pi the set of clocks (pi) to be set is determined (by module (A) in Figure 1) and the set of possible next edges is computed according to the inference rules of Table1 (by module (B)). To compute the next valuation we only need to keep track off the last valuation vi.... ..."

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