Time-Event based processing, a Survey Bruce Jones Vanessa Wallace

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1 Time-Event based processing, a Survey Bruce Jones Vanessa Wallace 1. Introduction Event based processing is used in many computational processes, whether by intent or as a result of the task requirement. Event processing can be subdivided into two methodologies; conservative a methodology that requires all inputs to be known before further processing, and optimistic a methodology that allows for speculative processing. This paper will primarily cover the optimistic model, though it will also cover some of the advances in conservative processing Relevance When optimistic event processing is mentioned, it is generally mentioned in the context of simulation. This is not the only context for optimistic or conservative event processing. Event processing is involved in most of the programs written. When most programs are invoked, procedures called, assembly language instructions executed; this is a form of event processing. The event being the invocation. Under optimistic processing, the form it might take is; invoking a program without all of the files or data present, calling a procedure without all of the arguments present or executing an assembly language instruction without needed intermediate calculations complete. The latter is most evident in the form of pipelined microprocessors that use branch prediction, and retirement of incorrect results. 2. Synchronous conservative event processing 2.1. Overview Conservative event processing ends up being the most intuitive to design, build and run. It is based upon the concept of a logical process taking the most recent input event and applying it to the process to which it belongs. Processes are not allowed to create events that exist in an earlier virtual time than the current virtual time of the executing process (a future event can not affect a past event). Because it is the earliest event and all processing is complete at that time. Though it is the most intuitive to design, build and run with single execution threads, implementation on a multithreaded environment becomes problematic. The problem is derived from guaranteeing causality. All of the events for a given process have to be available before the process is to be allowed to run. This requires either a segment that coordinates all tasks, or a methodology that allows tasks to know when causality is guaranteed, without requiring a synchronizing task. Using a single coordinating point for events creates a bottleneck. At its worse case, this design will degrade to single threaded operation regardless of the number of processors. The conservative protocols are intuitive, except when trying to spread across multiple processors. They are easy to implement on single processor design oriented towards single processor architectures (serial processing). The processing includes queue of events, where the most recent event is processed and output events go back onto queue(s) The Chandy-Misra-Bryant algorithm The conservative algorithm by Chandy and Misra and Bryant [36] uses a distrubuted-time scheme that allows elements to execute whenever they are ready in an attempt to exploit more parallelism in logic simulations. The extra parallelism comes at the cost of more complex element evaluations and the cost of deadlocks. Once the deadlock has been detected, it is resolved by finding the minimum event time of all unconsumed events in the system. Its base methodology is simple. The algorithm is straightforward to implement with simple control and data structures. CMB performs well as long as all static channels are equally utilized. Large dispersion of events in space and time is not bothersome. In addition, memory consumption is conservative.

2 One of the disadvantages of the CMB algorithm is the high cost of maintaining time synchronicity on a distributed system. There has to be a global control point or a method of agreeing upon current/next GVT amongst distributed systems. This conservative CMB algorithm does not maximize parallelism because of single point of timing control (or arbitration which has a high message overhead). In addition, synchronization mechanism is processor blocking, as a consequence prone to deadlock situations. The processing can not easily handle output of the type where generated event times are not monotonically increasing (time delay generated events). This is because input event times are used by the LPs to generate the LVTH to know whether to continue processing events. A way around this is to generate a message to ones self, indicating that output value x is to be generated after a time delay Null Messages Deadlock in CMB algorithm is avoided by transmitting the null message, [37]which is used to announce the absence of real message. Thus, when receiving a null message, an LP knows it can not receive any real messages from the corresponding incoming link until the time stamped on the null message. Processing of a null message, therefore, just simply resets the link-lock value of the incoming link. Since deadlock in parallel simulation are usually caused by feedback loops in the simulation network, to break the deadlock, usually an enormous number of null messages must be transmitted along these loops. However, in some cases, an LP need not to be blocked if the feedback loop can be detected The Carrier-Null Message Algorithm The Carrier-Null Message algorithm is developed by Cai and Turner[37] to detect the existence of feedback loops during the course of the simulation, and to improve the lookahead of the simulation upon the discovery of the feedback loop. The feedback loop detection and the lookahead improvement make uses of a special protocol message -- carrier-null message. Similar to the CMB algorithm, carrier-null message algorithm also consists of five sequential steps: input, simulation, computation 1, output, and computaion 2. Carrier-null message works different from CBM algorithm in Simulation and Output Steps as described in Cai and Turner [37]. However, the Carrier-Null message algorithm only deals with certain feed-backward networks. More complicated strategies need to be developed in order to efficiently exploit the algorithm. (e.g. the simulation on a LP network with multi-hierarchical feedback loops) Time Windows Based on a provably efficient scheduler for multithread programming, a predictable and robust conservative algorithm was also developed by Cai and Turner [38]. The simulation involves a divide and conquer style of execution which does not require the use of null message or deadlock detection. The algorithm is therefore robust, in that it can be used for simulation applications where local lookahead is small or zero or where lookahead information is difficult to extract. Although local lookahead information can be exploited, the algorithm is robust in that it also involves a global calculation of the time up to which events may be processed safely. The algorithm is novel in a way that it incorporates both local and global information in calculating the SafeTime for each LP. As a result, good speed-up was obtained when the average parallelism is large compared to the number of processors. Cai and Turner s Dag Consistent Parallel Simulation algorithm is further improved by Lim, Low, and Turner[39] on to modify the SafeTime computation a virtual factory simulation platform. It was found that SafeTime computation can be relaxed further to potentially allow more events to execute within a super-step. There are two advantages aspects in this modified algorithm. First it is simple to incorporate lookahead values in the SafeTime computation to dramatically reduce the number of super steps needed. Second, external events from LP I are no longer constrained to generated in timestamp order. 3. Synchronous optimistic event processing.

3 3.1. Overview Optimistic event scheduling was implemented in response to problems in conservative event execution when it comes to parallel execution. The greatest cost in conservative execution was the guarantee of causality. If causality was relaxed, but ensured through correction, execution of a hypothesized input value could improve execution times should the hypothesized input value be correct. In some instances, the output of the process might not change if the hypothesized input was incorrect. To ensure causality through correction, there would have to be a mechanism of recovering past states should the hypothesized value prove to be incorrect. The Time-Warp Operating System[28] was proposed upon this principle Time-Warp Time-Warp incorporates a single input queue of input events. Events are processed in lowest event timestamp first order. Output events are not buffered because there is no requirement that output events occur in time-increasing order as on the Chandy-Misra[36] conservative system. A physical process keeps track of its local virtual time, which is derived directly from the input queue s event time. Should a process discover that its local virtual time is older than the time of an event on the input event queue, the executing process knows that it has processed events out of time order and has a causality violation. Time-Warp corrects the causality violation by rolling back to an earlier state and in the process creating anti-messages to cancel any incorrect output that it generated. The rollback and the costs associated with maintaining the information to be able to rollback are the greatest costs associated with the Time-Warp optimistic event processing. Rollbacks not only invalidate physical process results, through the anti-messages, rollbacks can cause other events to also invalidate the results of other physical processes and potentially cause a cascade of rollbacks. Invalidation of processing causes the execution to occur again with new data, and potentially different results. There is also a significant amount of storage required to support the rollback mechanism. For each state that the physical process goes through, all state variant data has to be stored as well as a copy of the outbound result event and the input event that caused the transition Overview of what is going on to combat weaknesses. There have been several methods proposed and tested, to deal with Time-Warp s tendency to consume processor utilization on calculations that will later be invalidated, costs of rollback, memory consumption and network bandwidth usage between LPs. These include moving window based optimization, lazy/aggressive/adaptive cancellation, control of checkpointing intervals Reduction in rollback costs Aggressive Cancellation - Wilsey[1][3] Aggressive cancellation on rollback makes the assumption that most of the output values will change when executing back to the local virtual time before rollback was caused. The concept is to get the antimessages out to cancel the erroneous output before any other physical processes use it as an input in calculations. To do this, all anti-messages are generated when rolling back, before any re-execution of events is done. This method works fairly well when a process runs as a series of states (state machine) which use input events to transition to different states, output being generated at the new states. It doesn t work well when physical process models a single step function with little or no time lag Lazy Cancellation - Wilsey[1][3] Lazy cancellation on rollback, makes the assumption that little if any of the output will change if a new event is added to the sequence. The concept is to delay sending anti-messages until it is confirmed that the output is incorrect to avoid causing other physical processes to rollback. As a result, the process rolls back and starts executing the modified input event list. If any output events are changed in the process of re-execution, anti-messages are sent out followed by the corrected output event if any. If the result of the

4 re-execution is that there is no change in the output message, nothing is changed and the previous output message is left unchanged. If the result of the re-execution is that there is no output message for the virtual time where the previous execution produced an output message, an anti-message is sent out to cancel the erroneous message and no new message is created. While this technique is effective with nonstate machine processes, it has the potential to cause larger rollbacks on dependant processes by letting them execute further in virtual time before being corrected Adaptive Cancellation - Wilsey[1][3] Adaptive cancellation presented in the Wilsey[3][1] paper is designed to attack the problem of having to predefine cancellation strategies of a physical process at startup. To be able to statically define the optimal cancellation strategy before run-time requires perfect knowledge of the execution environment. In addition, static policies do not allow for adaptation should the execution environment change part way through the execution. It my be the situation where an aggressive cancellation may most effect at first, but during later execution, lazy cancellation may be more effective. According to Wilsey[3][1], during tests, it was found that the optimal strategy was sensitive to how the physical processes were partitioned into logical processes{partitioning scheme}. Adaptive cancellation allows a process to determine which cancellation strategy to use based upon run-time metrics. The adaptation algorithm works by calculating a hit ratio. The hit ratio is essentially the percentage of rolledback output messages where the output did not change. To prevent undue overhead, the sample set depth{filter Depth} is defined at startup. The filter depth is the number of output message comparison results to store for calculating the hit ratio. Two thresholds are defined. A2L_Threshold is the hit ratio threshold at which the algorithm will switch from aggressive to lazy cancellation{a2l}. L2A_Threshold is the threshold at which the algorithm will switch from lazy to aggressive cancellation. The value for A2L_Threshold must be greater or equal to the value for L2A_Threshold. Rapid switching between lazy and aggressive cancellation is prevented by a large filter depth{to reduce statistical variance}, infrequent invocation of the control mechanism and the creation of hysteresis in the switching values by making A2L_Threshold unequal to L2A_Threshold. Testing by Wilsey[3][1] indicated that adaptive cancellation could operate as efficiently(by measuring execution time) as an optimally chosen cancellation protocol Reduction of Memory Footprint One of the greatest consumers of resources in the Time-Warp system, is the usage of memory for rollback state information, input event storage and stored output messages. Because input event storage is needed for calculating forward after a rollback, and the copy of output messages is needed to identify any antimessages that need to be sent out, most of the development has covered methods for reducing the spaced used for copies of physical process states{check-points} Pruneback This is a mechanism that Preiss & Loucks[15] proposed to use to handle memory usage when the system was at or near the limit for available memory {memory stall}. It is not a method to minimize memory usage, but a method to make it more probable that execution will complete by freeing up used but non critical memory allocation. In comparison to Artificial Rollback and Cancelback mechanisms, it promises to allow limited memory recovery while not forcing physical processes to backup in virtual time as does Cancelback and Artificial Rollback. The Pruneback mechanism is based upon recovering needed memory from the saved state information of the physical process. If a rollback occurs to the now missing state, it ends up rolling back to a the first virtual time state before the missing state, and then coasting forward using the saved input events to recalculate that state. There are constraints to pruning back. Neither the physical processes nor the GVT state are to be pruned. Preiss & Loucks[15] left the selection of which states beyond the constraints for the Pruneback mechanism, to be implementation dependent Periodic checkpointing Periodic check-pointing was originally proposed by Jefferson[28] as a way to reduce the state saving

5 overhead of the Time-Warp system. The original paper did not go any further into periodic checkpointing at that time Adaptive checkpointing. Non-Linear feedback control Finding that the Periodic checkpoint algorithm of Lin, Preis, Loucks & Lazowska[2] to be computationally complex, and having the possibility of the gains being offset by the cost of computation, Fleischmann & Wilsey[6] proposed a simpler heuristic algorithm based upon supervisory control in control theory. The heuristic tries to balance two types of overhead, the cost of saving states vs. the cost of coasting forward over unsaved states. A cost function is derived from the sum of the cost of saving states and cost of coasting forwards. The checkpoint interval is recalculated every N intervals (typically 100), if the previous step was to increase the interval, and if the cost function was observed to actually increase, the checkpoint interval will be decremented by one. If the cost function was observed to decrease, the checkpoint interval will be further incremented. The heuristic algorithm is symmetric if the previous step was to decrease the checkpoint interval. Effectively the heuristic works as a local minimum search in process control. Because the heuristic is applied at run-time, it is also capable of handling dynamic changes in rollback and checkpoint behavior Reverse Computation instead of State Saving. Considering that considerable overhead might be involved in saving state, Carothers[20] took the approach have treating the physical processes as being potentially reversable. Rolling back would be accomplished by using the present state and the saved input events to apply inverse operations to the present state to arrive at the rolled back state. In the event that the operation was not completely reversible (ie: a destruct operation) the potential of saving partial state information for the non-reversible portions of the process in the output events was used. A reversible random number generator was also created with a period of since some processes require a pseudo random calculation for event triggered probabilistic events. The reversible physical processes were written by hand, but a mechanism for compiler generating the inverse operations was diagrammed. A side effect of using the reversible approach was discovered in the form of greatly increased speed. In testing, Carothers was using an SGI SMP architecture. Using a hardware profiler on the machine to track the benefit, they found that the smaller memory footprint reduced TLB and cache misses Non checkpointing of Non-state machine elements{rollback Relaxation}[7] Wilsey, Palaniswamy & Aji[7] proposed a method by which memoryless physical processes do not have to store past state data. They separated physical processes into two categories; memoried output events are defined by both input event values and internal state values {remembered history of values, before their present value}, and memoryless process whose output events are directly determined by the values of its input events. To implement this scheme, the input events were sorted into two sets of input queues. They were sorted both by the variable they effect category and the arrival time. This allowed the physical process to determine the input values on a rollback by looking directly at all input events with a previous time to the rollback causing event and proceed forwards from that point. 4. Summary Conservative methods of processing were included in this survey for two reasons. First, conservative methods are the primary way events {data} is processed, including in parallel systems. Second, because Time-Warp or optimistic event processing was an enhancement on the original Chandy-Misra[36] algorithm. In terms of looking towards the future, there will be a greater emphasis on optimistic processing techniques. This will be in part due to electrical transmission limitations. What is meant by limitations, is that as processor clocks run faster, they become more like radio transmitters. As frequencies reach into the Gigahertz, a small trace on a motherboard, 3 inches long, becomes a full wave antenna. This trace, acting as an antenna, will bleed out signal power, be more sensitive to inductive coupling and cause the signal transmitted to be distorted (need about 3 orders of Nyquist resolution to pass a reasonable squarewave. 3 rd Nyquist is the 3 rd harmonic). This will force the usage of loosely

6 coupled parallel systems to solve problems, and conservative processing has the demonstratable tendency to limit parallel processing in its synchronization and causality verification. 5. Future directions for research in the area of Parallel Discrete Event Processing High Level Architecture The High Level Architecture (HLA) which provides the specification of a common technical architecture for use across all classes of simulation in the U.S. Department of Defense. It is currently in the process of being applied with simulation developed for analysis, training, and evaluation. Both the Object Management Group and the IEEE are incorporating HLA into industry standards for distributed simulation. It is foreseeable that researchers in parallel discrete event simulation will be faced with technology challenges which arise in the future implementation and the application of HLA. There will be more research projects that are similar to Fujimoto's project (PDAS group in Georgia Tech) to provide a time management support in both conservative and optimistic synchronization among the simulations in High Level Architecture The rise of Web-based Simulations The World-Wide-Web is revolutionizing the computer industry. Recent advances in Web technology have made the Web a viable mechanism for performing, and distributing simulation. In addition, Java has been considered by most researchers as uniquely suitable to implement advanced architectures for discrete-event simulation. We predict that web-based simulators which take advantage of the capacity of web-based simulation and techniques to improve an object-oriented environment for fast simulation will remain the focus of research in the near future. Furthermore, the integration of High Level Architectures with Web technologies will be a challenging and interesting area for future research Telecommunication and wireless networks While a large amount of Parallel Discrete Event Simulation research has focused on employing multiprocessors and multicomputers, the use of a network of workstations interconnected through Ethernet or ATM has evolved into a popular and effective platform for Parallel Discrete Event Simulation. However, performance evaluation conducted on an advanced version of Time Warp(GTW) has shown that the performance of the GTW is degraded in the network computing environments. Some work have been done on PDES systems to improve simulation performance. We predict that more work on both conservative and optimistic synchronous methods will be demanded to improve simulation performance in ATM networks, cellular networks and large-scale wireless networks Time Warp optimizations For the present, researchers are still faced with the challenges of Time Warp's optimistic synchronization. As mentioned in this survey, the disadvantages of optimistic synchronization are: the high cost in maintaining validity of results, potential to spend CPU cycles on computations that will be thrown away as a result of invalidation of input values on a roll-back, the large memory footprint caused by saving states, results, and inputs between Local Virtual Time and Global Virtual Time for each process. Needless to say, future research will continue to investigate various optimization techniques for Time Warp systems. The future direction will continue to focus on efficient GVT computation, memory management, incremental state saving, etc. BIBLIOGRAPHY Note: The entries marked by an underline are papers that we have had an opportunity to read through and use. Due to time/availability constraints, we were not able to go through all of them. These papers

7 not marked are on our search horizon. The initial intent was to use MSWord s end note capability to be able to dynamically remove and renumber the references at the end of building the paper. Unfortunately MSWord failed us on that one. Because removing the papers would be a non-value-added operation, they were left in, but not underlined. The order of the listing of the bibliography was left title first. 1. On-Line Configuration of a Time Warp Parallel Discrete Event Simulator Radharamanan Radhakrishnan, Nael Abu-Ghazaleh, Mololan Chetlur Philip A. Wilsey Dept of ECES, PO Box Cincinnati University Cincinnati OH Proceedings of the 1998 International Conference on Parallel Processing August 10-14, 1998 ISBN Selecting the checkpoint interval in time warp simulation. Y.B.Lin, B.R. Preiss, W.M.Loucks, E.D.Lazowska Proceedings of the 7 th Workshop on Parallel and Distributed Simulation (PADS), pages Society for Computer Simulation, July Feedback Control in Time Warp Synchronized Parallel Simulators Philip A. Wilsey Dept of ECES, PO Box Cincinnati University Cincinnati OH First International Workshop on Distributed Interactive Simulation and Real Time Applications, An Analytical Comparison of Periodic Check-Pointing and Incremental State Saving A. Palaniswamy, P. A. Wilsey Society for Computer Simulation{PADS 93}, July 1993, pages Adaptive Check-Pointing in Time Warp R.Ronngren and R. Ayani Proceedings of the 8 th Workshop on Parallel and Distributed Simulation{PADS 94}, pages , Society for Computer Simulation. 6. Comparative Analysis of periodic state saving techniques in time warp simulators. J. Fleischmann, P.A.Wilsey Proceedings of the 9 th Workshop on Parallel and Distributed Simulation {PADS 95}, pages 50-58, June Rollback Relaxation: A Technique for Reducing Rollback Costs in Optimistically Synchronized Parallel Simulators Philip A. Wilsey, Avinash Palaniswamy, Sandeep Aji Center for Digital Systems Engineering University of Cincinnati, Cincinnati OH Proceeding of the International Conference on Simulation and Hardware Description Languages, SHDL The adaptive Time-Warp concurrency control algorithm. D. Ball & S. Hoyt Distributed Simulation pgs , Society for Computer Simulation, Jan Adaptive bounded time windows in an optimistically synchronized simulator. Palaniswamy & P.A. Wilsey Third Great Lakes Symposium on VLSI, pages , Performance evaluation of the bounded Time Warp algorithm S.J. Turner and M. Q. Xu. Proceedings of the SCS Multiconference on Parallel and Distributed Simulation 24(3): , A performance study of the cancelback protocol for time warp S.R.Das & R.M. Fujimoto Proceedings of the 7th Workshop on Parallel and Distributed Simulation. Jul 1993 pages An adaptive memory management protocol for Time Warp parallel simulation. S.R.Das and R.M.Fujimoto "Sigmetrics", pgs , May Investigations in adaptive distributed simulation. D. O. Hamnes and A. Tripathi. Proceedings of the 8th Workshop on Parallel and Distributed Simulation PADS(94)" pages Society for Computer Simulation, July Optimal Memory Management for Time Warp Parallel simulation. Y.B. Lin & B.R.Preiss. ACM Transactions on Modeling and Computer Simulation, 1(4): , Oct 1991.

8 15. Memory Management Techniques for Time Warp on a Distributed Memory Machine Bruno R. Preiss, Wayne M. Loucks Department of Electrical and Computer Engineering University of Waterloo, Waterloo ON N2L 3G1 {Ontario, Canada} The Institute of Electrical and Computer Engineers, Optimistic Fossil Collection for Time Warp Simulation Christopher H. Young, Philip A. Wilsey Computer Architecture Design Laboratory Dept. of ECES, PO Box , Cincinnati OH Proceedings of the Hawaiian International Conference on System Sciences HICSS Optimism: Not Just For Event Execution Anymore Christopher H. Young, Radharamanan Radhakrishnan, Philip A. Wilsey Dept of ECES, University of Cincinnati, Cincinnati OH th Workshop on Parallel and Distributed Simulation, PADS Performance Benefits of Optimism in Fossil Collection Christopher H. Young, Radharamanan Radhakrishnan, Philip A. Wilsey Dept. of ECES, University of Cincinnati, Cincinnati OH Proceedings of the Hawaii International Conference on System Sciences, HICSS Dynamically Switching between Lazy and Aggressive Cancellation in a Time Warp Parallel Simulator Raghundandan Rajan, Philip A. Wilsey Center for Digital Systems Engineering Dept. of ECE, PO Box , University of Cincinnati, Cincinnati OH Proceedings of the 28 th Annual Simulation Symposium, ASS Efficient Optimistic Parallel Simulations using Reverse Computation Christopher D. Carothers, Dep. Computer Science Rennselaer Polytechnic Institute Kalyan S. Perumalla & Richard M. Fujimoto, College of Computing, Georgia Inst. Tech. <No indicated publication > 21. A Control Mechanism for Parallel Discrete Simulation L. M. Sokol, B. K. Stucky, V. S. Hwang Proceedings of the 1989 International conference on Parallel Processing, Vol 3, pp , Performance evaluation of the bounded Time Warp Algorithm S. Turner M. Xu Proceedings of the 6 th Workshop on Parallel and Distributed Simulation pp , Concurrency Preserving Partitioning(CPP) for Parallel Logic Simulation Hong. K. Kim, Jack Jean Proceedings of the 10 th Workshop on Parallel and distributed Simulation, pp98-105, Load Balancing and Work Load Minimization of Overlapping Parallel Tasks V. Krishnaswamy, G. Hasteer, P. Banerjee Proceedings of the 1997 International Conference on Parallel Processing, Aug Asynchronous Distributed Simulation via a Sequence of Parallel Computations K. M. Chandy, J. Misra Communications of the ACM, Vol 24, No 11, pgs April Parallel and Distributed Simulation of Discrete Event Systems Alois Ferscha Contributed to Handbook of Parallel and Distributed Computing, McGraw-Hill, 1995 NOTE: This one had a detailed summary of different mechanisms, though from a simulation point of view. 27. Distributed Discrete-Event Simulation J. Misra ACM Computing Surveys, 18(1):39-65, Distributed Simulation and the Time Warp Operating System David Jefferson, Brian Beckman, Fred Wieland, Leo Blume, Mike DiLorento, Phil Hontalas, Pierre Laroche, Kathy Sturdevant, Jack Tupman, Van Warren, John Wedel, Herb Younger, Steve Bellenot NOTE: Original Class article. 29. Parallel Discrete-Event Simulation of FCFS Stochastic Queuing Networks. D. M. Nicol Proceedings of the ACM/SIGPLAN APPEALS 1988, pgs Algorithms for distributed termination detection F. Mattern Distributed Computing, 2: , Distributed Deadlock Detection K. M. Chandy, J. Misra, L. M. Haas ACM Transactions on Computer Systems, 1(2): , May Bounded Lag Distributed Discrete Event Simulation. B. D. Lubachevsky Proceedings of the SCS Multiconference on Distributed Simulation 19(3) pgs SCS, Feb1988

9 33. An Algorithm for Distributed Discrete-Event Simulation The Carrier Null Message Approach Wentong Cai, Steven J. Turner Proceedings of the SCS Multiconference on Distributed Simulation Vol 22(1), pages 3-8. SCS January An Algorithm for Reducing Null-Messages of CMB Approach in Parallel Discrete Event Simulation Wenton Cai, Steven J. Turner 35. OFC: A Distributed Fossil-Collection Algorithm for Time-Warp Christopher H. Young, Nael B. Abu-Ghazaleh, Philip A. Wilsey Proceedings of the 12 th International Conference on Distributed Computing DISC An Evaluation of the Chandy-Misra-Bryant Algorithm for Digital Logic Simulation Larry Soule and Anoop Gupta, Computer Systems Laboratory, Standford University, CA Distributed Simulation, Volume 24(2), Pages , California, SCS. Simulation: a Predictable and Robust Conservative. 37. An Algorithm For Reducing Null-Message of CMB Approach in Parallel Discrete Event Simulation. Wentong Cai, Stephen J. Turner Dag Consistent Parallel Simulaition 38. Dag Consistent Parallel Simulation: a Predictable and Robust Conservative Algorithm Wentong Cai, Stephen J. Turner 39. Relaxing SafeTime Computation of a Conservative Simulation Algorithm Chu-Cheow Lim, Yoke-Hean Low, and Stephen J. Turner