### Table 1 Discrete-event simulation algorithm for stochastic event structures.

"... In PAGE 11: ... It is not di cult to check that the above described discrete-event system for stochastic event structure is a time-homogeneous GSMP. The complete simulation algorithm for stochastic event structure hE;A;Ri with E = (E;#;7!;l) is presented in Table1 . For random variable U with distribution FU let FU( ) denote a sample of U; output state si = (Ei;Ri;Hi), for i gt; 0.... ..."

### Table 3: Discrete transitions and resets.

"... In PAGE 5: ... The possible events are listed in the Table 2. Let in = ;; env = f ar; d0; d1g; cd = f mid; depg; int = f up0; up1g; out = = env [ cd [ int: The discrete transitions are described in Table3 . The rst entry in Table 3 should be read as: If at time t the system is at discrete state q1 and at continuous state xq1, if at that time event ar occurs, then the system moves to discrete state q2 and continuous state xq2 where the rst component of xq2, denoted by xq2;1, is set to the value 0 and the second component is set to the value xq1;2.... In PAGE 5: ... The rst entry in Table 3 should be read as: If at time t the system is at discrete state q1 and at continuous state xq1, if at that time event ar occurs, then the system moves to discrete state q2 and continuous state xq2 where the rst component of xq2, denoted by xq2;1, is set to the value 0 and the second component is set to the value xq1;2. In Table3 the transitions from the discrete states q5; q6; q7; q8 have been omitted because they correspond in an obvious way to those displayed above. The environmental events from the set env can occur at all states.... In PAGE 5: ... Control of the belt will prevent these events from happening at the discrete states q2 and q4. Therefore these transitions have been omitted from Table3 . The discrete event system associated with the hybrid control system is partly displayed in Figure 2.... ..."

### Table 3: Discrete transitions and resets.

"... In PAGE 3: ... The possible events are listed in the Table 2. Let #06 in = ;; #06 env = f#1B ar ;#1B d0 ;#1B d1 g; #06 cd = f#1B mid ;#1B dep g; #06 int = f#1B up0 ;#1B up1 g; #06 out =#06=#06 env #5B #06 cd #5B #06 int : The discrete transitions are described in Table3 . The #0Crst entry in Table 3 should be read as: If at time t the system is at discrete state q 1 and at continuous state x q 1 , if at that time event #1B ar occurs, then the system moves to discrete state q 2 and continuous state x q 2 where the #0Crst component of x q 2 , denoted by x q 2 ;1 , is set to the value 0 and the second component is set to the value x q 1 ;2 .... In PAGE 3: ... The #0Crst entry in Table 3 should be read as: If at time t the system is at discrete state q 1 and at continuous state x q 1 , if at that time event #1B ar occurs, then the system moves to discrete state q 2 and continuous state x q 2 where the #0Crst component of x q 2 , denoted by x q 2 ;1 , is set to the value 0 and the second component is set to the value x q 1 ;2 . In Table3 the transitions from the discrete states q 5 ;q 6 ;q 7 ;q 8 have been omitted because they correspond in an obvious way to those displayed above. The environmental events from the set #06 env can occur at all states.... In PAGE 3: ... Control of the belt will prevent these events from happening at the discrete states q 2 and q 4 . Therefore these transitions have been omitted from Table3 . The discrete event system associated with the hybrid control system is partly displayed in Figure 2.... ..."

### Table 3: Discrete transitions and resets.

1997

"... In PAGE 5: ... The possible events are listed in the Table 2. Let n06 in = ;; n06 env = fn1b ar ;n1b d0 ;n1b d1 g; n06 cd = fn1b mid ;n1b dep g; n06 int = fn1b up0 ;n1b up1 g; n06 out =n06=n06 env n5b n06 cd n5b n06 int : The discrete transitions are described in Table3 . The n0crst entry in Table 3 should be read as: If at time t the system is at discrete state q 1 and at continuous state x q 1 , if at that time event n1b ar occurs, then the system moves to discrete state q 2 and continuous state x q 2 where the n0crst component of x q 2 , denoted by x q 2 ;1 , is set to the value 0 and the second component is set to the value x q 1 ;2 .... In PAGE 5: ... The n0crst entry in Table 3 should be read as: If at time t the system is at discrete state q 1 and at continuous state x q 1 , if at that time event n1b ar occurs, then the system moves to discrete state q 2 and continuous state x q 2 where the n0crst component of x q 2 , denoted by x q 2 ;1 , is set to the value 0 and the second component is set to the value x q 1 ;2 . In Table3 the transitions from the discrete states q 5 ;q 6 ;q 7 ;q 8 have been omitted because they correspond in an obvious way to those displayed above. The environmental events from the set n06 env can occur at all states.... In PAGE 5: ... Control of the belt will prevent these events from happening at the discrete states q 2 and q 4 . Therefore these transitions have been omitted from Table3 . The discrete event system associated with the hybrid control system is partly displayed in Figure 2.... ..."

### (Table 1) and the average queueing delay experienced by the two streams of ABR cells at the bottleneck output link (Ta- ble 2) and compared the results with three other systems; a discrete event simulation (BONeS) [11], a non-proportional time version of our system where all devices are physical [10], and a Time Warp simulation (GTW) [3, 5, 6].

### Table 5 Possible events for the transport of glucose across the BBB endothelium in the systems simulation

2005

"... In PAGE 15: ... Deviating from continuous mathematics, the simulation correlates biological events as linked sets, each with discrete probabilities. Table5 shows other possible events in the glucose transport system at the endothelium. Fig.... ..."

### Table 2: Levels of System Specification in JSLIRS Formalization.

"... In PAGE 8: ... Threads Left No Yes Interpret section as set of rules and variables Add variables and rules to repository Repository constitutes a System specification at level 4 Formalize Rules and Variables in executable form Repositoryplus rule engine constitutesa System specification at level 3 Populate testable Schemas of I/O Function Testable form of I/O Function constitutesa System specification at level 2 Instantiate Schemas using Rule engine Instantiated schemas Constitutetest models Figure 4. Formalization of the Joint Single Link Requirements Specification Table2 relates the process of representing the JSLIRS specification as a DEVS (as outlined in Figure 4) to the Hierarchy of System Specification discussed earlier. Each thread is interpreted as a set of condition-action rules with suitable for describing discrete event systems [15,16].... ..."

### Table 3: Predicate and Function for Input Gate `IG1 apos;

"... In PAGE 3: ... The action for each case has been speci#0Ced in the output gate functions. Thus, the iden- tity function is used in `IG1 apos; #28see Table3 #29 to signify that no action is to be taken by that gate. 3 UltraSAN UltraSAN is a tool for model-based evaluation of discrete event systems described by stochastic activity networks.... ..."

### Table 1: Simulation vs. discrete{time analysis: E[W ] Simulation Analysis

1999

"... In PAGE 8: ... Note the bath tub-like shape of the waiting time curve, which is characteristic for batch service systems. In Table1 , the mean waiting times gained from continuous{time discrete{event sim- ulation are given. We compare them to the values derived with our proposed method.... ..."

Cited by 2

### Table 1: Simulation vs. discrete{time analysis: E[W ]

1999

"... In PAGE 8: ... Note the bath tub-like shape of the waiting time curve, which is characteristic for batch service systems. In Table1 , the mean waiting times gained from continuous{time discrete{event sim- ulation are given. We compare them to the values derived with our proposed method.... ..."

Cited by 2