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A new mathematical model for optimizing the performance of parallel and discrete event simulation systems

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Conference Paper

A new mathematical model for optimizing the performance of parallel and discrete event simulation systems

Abstract

Null message algorithm is an important conservative time management protocol in parallel discrete event simulation systems for providing synchronization between the distributed computers with the capability of both avoiding and resolving the deadlock. However, the excessive generation of null messages prevents the widespread use of this algorithm. The excessive generation of null messages results due to an improper use of some of the critical parameters such as frequency of transmission and Lookahead values. However, if we could minimize the generation of null messages, most of the parallel discrete event simulation systems would be likely to take advantage of this algorithm in order to gain increased system throughput and minimum transmission delays. In this paper, a new mathematical model for optimizing the performance of parallel and distributed simulation systems is proposed. The proposed mathematical model utilizes various optimization techniques such as variance of null message elimination to improve the performance of parallel and distributed simulation systems. For the sake of simulation results, we consider both uniform and non-uniform distribution of Lookahead values across multiple output lines of an LP. Our experimental verifications demonstrate that an optimal NMA offers better scalability in parallel discrete event simulation systems if it is used with the proper selection of critical parameters.
Keywords: Parallel and distributed systems, discrete event
simulation, null message algorithm.
Abstract
Null message algorithm is an important conservative time
management protocol in parallel discrete event simulation
systems for providing synchronization between the distributed
computers with the capability of both avoiding and resolving
the deadlock. However, the excessive generation of null
messages prevents the widespread use of this algorithm. The
excessive generation of null messages results due to an
improper use of some of the critical parameters such as
frequency of transmission and Lookahead values. However, if
we could minimize the generation of null messages, most of the
parallel discrete event simulation systems would be likely to
take advantage of this algorithm in order to gain increased
system throughput and minimum transmission delays. In this
paper, a new mathematical model for optimizing the
performance of parallel and distributed simulation systems is
proposed. The proposed mathematical model utilizes various
optimization techniques such as variance of null message
elimination to improve the performance of parallel and
distributed simulation systems. For the sake of simulation
results, we consider both uniform and non-uniform distribution
of Lookahead values across multiple output lines of an LP.
Our experimental verifications demonstrate that an optimal
NMA offers better scalability in parallel discrete event
simulation systems if it is used with the proper selection of
critical parameters.
1. INTRODUCTION
While there is a considerable literature exploring how poor
selection of critical parameters might results poor performance
of PDES systems [8, 12], surprisingly little work has examined
how critical parameters impact on the performance of PDES
systems. These research works indicate the strong relationship
among many critical parameters such as Lookahead and
frequency of transmission that one may use to quantify the
impact of these parameters on the PDES performance. None of
these research works, however, evaluate the determinants of
the critical parameters to the performance of PDES systems.
This paper presents a mathematical model to optimize the
performance of PDES systems by minimizing the null message
transmission across each LP using various optimization
techniques.
In parallel discrete event simulation (PDES) systems, the
distributed discrete events need to be tightly synchronized with
each other in order to work simultaneously on different parts of
a common task. However, if these discrete events are not
properly synchronized, the performance of a PDES
environment may degrade significantly [2]. Time management
algorithms (TMA) are, therefore, required to ensure that the
execution of a PDES is properly synchronized. In general,
synchronization protocols can be categorized into two different
families: conservative and optimistic. In optimistic algorithm,
both deadlock detection and recovery occur at run time.
However, if it is used in a wide range parallel network, each
logical process (LP) may experience longer transmission
delays at run time [13]. On the other hand, conservative
protocols fundamentally maintain causality in event execution
by strictly disallowing the processing of events out of
timestamp order. In order to avoid and resolve the deadlock
situations, each LP needs to exchange time stamp information
with the other neighboring LPs [1, 3]. Examples of
conservative mechanisms include Chandy, Misra and Byrant's
NMP [6], and Peacock, Manning, and Wong [11] avoided
deadlock through null messages.
Conservative TMA can be further classified as synchronous
and asynchronous protocols [1]. Synchronous algorithm uses
global synchronization mechanism to determine the minimum
time stamp of each incoming event for an LP. On the other
hand, NMA is an example of an asynchronous conservative
algorithm that does not require global synchronizations. The
primary problem associated with null messages is that if their
timestamps are chosen inappropriately, the simulation becomes
choked with null messages and performance suffers. Some
intelligent approaches to null message generation include
generation on demand [8], and generation after a time-out [5].
Some earlier research on discrete event simulation has focused
on variants of null message protocol (NMP, with the objective
of reducing the high null message overhead. For instance, Bain
A New Mathematical Model for Optimizing the Performance of Parallel and
Discrete Event Simulation Systems
Syed S. Rizvi and Khaled. M. Elleithy
Computer Science and Engineering Department
University of Bridgeport
Bridgeport, CT 06601
{srizvi, elleithy}@bridgeport.edu
Aasia Riasat
Department of Computer Science
Institute of Business Management
Karachi, Pakistan 78100
aasia.riasat@cbm.edu.pk
and Scott [4] attempt to simplify the communication topology
to resolve the problem of transmitting redundant null messages
due to low Lookahead cycles. Other recent developments [10]
have focused on incorporating knowledge about the LP into the
synchronization algorithms. Cota and Sargent [7] focused on
the skew in simulation time between different LPs by
exploiting knowledge about the LPs and the topology of the
interconnections.
Although, much research has been done to evaluate the
performance of conservative NMA for inefficiencies and
transmission overhead [3, 8, 12], none of them suggest any
potential optimization for the NMA. Reference [12] proposed a
new approach that shows relationships between many
parameters to quantify the performance of PDES system
running under NMA. It has been shown that the selection of
values for several critical parameters such as the values for
Lookahead, null message ratio (NMR), and frequency of
transmission plays an important role in the generation of null
messages [12]. If these values are not properly chosen by a
simulation designer, the result will be an excessive number of
null messages across each LP. This situation gets more severe
when the NMA needs to run to perform a detailed logistics
simulation in a distributed environment to simulate a huge
amount of data [9]. This paper presents a mathematical model
that implements many optimization techniques to optimize the
performance of NMA by minimizing the exchange of null
messages across the LPs. A significant improvement is
measured in the performance of PDES system in terms of
reduced execution speed and transmission delays.
The rest of the paper is organized as follows. Section 2
presents the proposed mathematical model. Section 3 provides
the implementation of various optimization techniques on the
NMA for improving the performance of PDES systems. The
numerical and simulation results are presented in Section 4.
Finally, we conclude in Section 5.
2. PERFORMANCE OPTIMIZATION THROUGH
PROPOSED MATHEMATICAL MODEL
Some of the important model variables, along with their
definition, are listed in Table I. For the sake of mathematical
model, we assume that the value of Lookahead may change
during the execution of a Lookahead period. However, a
sudden increase or decrease in the values of Lookahead during
the simulation can not be accepted. In addition, we assume that
each LP is initialized with a constant event arrival. However,
as the simulation progresses, we use both uniform and non-
uniform distribution of Lookahead values across multiple
output lines of each LP. For the frequency of message
transmission, we assume that all messages are equally
distributed among the LPs. Unless otherwise stated, we use the
term all messages to refer to both null and event messages.
Finally, we assume that a fixed size message is transmitted
between LPs.
Our proposed mathematical model is based on the internal
architecture of an LP as shown in Fig. 1 and Fig. 2. The
advancement in simulation time can be defined as a ratio of
performance to the event arrival rate. The number of event
messages processed per second per LP is represented by P,
where as the occurrence of the number of events per simulation
second is refereed as an even arrival rate and it is represented
by ρ. This leads us to the following mathematical expression of
the relative speed for advancement:
( )
Msg
T
s
PE
 
 
 
 
(1)
Taking this into account, we can give the following
hypothesis for approximating the number of null messages
transmitted per LP: If we assume that we have an average
value of Lookahead (L) which associates with one of the
output lines of an LP, then P can be approximated as”:
1
Msg
P E
L
 
 
 
(2)
Combining (1) and (2) yields the estimated number of null
messages transmitted per LP that has only one output line as
shown in (3).
( )
1 1
S
Msg S
LP
Msg
T
Null E T
L E L
 
   
 
   
 
   
 
(3)
Furthermore, if we assume that we have O number of output
lines attached with each LP with the uniform distribution of
Lookahead value on each output line, then (3) can be further
generalized for O number of output lines per LP as follows:
( )
S
Msg S
LP
Msg
T
Null E T
L E L
 
   
 
   
 
   
 
(4)
where O represents the total output lines per LP.
It should be noted that (4) represents total number of null
messages transmitted per LP via O number of output lines to
the neighboring LPs when the distribution of L is assumed to
be uniform per output lines. If we assume that we have m
number of total LPs present in a system where each LP has O
number of output lines, then this allows us to extend (4) and
generalize it for m number of LPs present in distributed
simulation as shown in (5). It can be evident that (5) gives total
TABLE I
System Parameter Definition
Parameter Definition
P
Computation required for processing an event per second
ρ
Event arrival rate (events per second)
MRT
Minimum receiving time
MST
Minimum sending time
L
Lookahead
STA
Simulation time advancement
F
T
Frequency of transmission
T
Null
Timestamp of a null message
T
S
Current simulation of a LP
T
Total
Total simulation time in seconds
number of null messages exchange among all LPs present in
the system.
( )
S
Msg S
m LP
Msg
T
O O
Null E m T m
L E L
 
   
 
   
 
   
 
(5)
where the term
O L
in (5) shows a uniform distribution of
Lookahead value for O number of output lines per LP and the
term m represents total number of LPs in the system.
The assumption of uniform distribution of Lookahead
among O output lines of an LP simplifies the procedure for
computing the number of null messages transmitted per LP to
other neighboring LPs. However, the values for Lookahead
may change during the execution of a Lookahead period that
makes the uniform distribution assumption of Lookahead a
little unrealistic. Based on this argument, we can rewrite (4) as:
( )
1 1
1
O O
Msg S
S
LP
i i
i Msg i
ET
Null T
L E L
= =
 
 
 
 
 
 
 
∑ ∑
(6)
It should be noted that (6) represents the total number of null
messages transmitted per LP to other neighboring LPs via O
number of output lines where each line can have a different
Lookahead value.
If we assume that the model is partitioned into m number of
total LPs where each LP can have at most O number of output
lines, then this allows us to extend (6) and generalize it for m
number of LPs. This generalization can be expressed in (7).
( )
1 1 1 1
1
m O m O
Msg S
S
m LP
h i h i
hi Msg hi
ET
Null T
L E L
= = = =
 
 
 
 
 
 
 
∑ ∑
(7)
It can be evident that (7) gives total number of null messages
exchange among all LPs present in the system.
3. PROPOSED OPTIMIZATION TECHNIQUES FOR
NMA
In this section, we first derive a closed form mathematical
expression for both frequency of transmission and the variance
of null message elimination that can be further used to
determine the reduction in the null message traffic in the
presence of deadlock. The derived closed form expression uses
the simple concept of frequency of transmission described in
[12] to minimize the exchange of null messages across the LPs.
In addition, we implement the optimization technique via
variance of null message elimination.
3.1. Optimization Via Frequency of Transmission
Instead of sending null messages after processing each event
on each output line of an LP, it should be transmitted with
respect to a certain frequency of transmission. This frequency
of transmission (FT) is a fixed amount of time and it should be
measured in simulation second per second. In other words, the
Lookahead value which is associated with one or more output
lines can be approximated as the frequency of transmission per
output line of an LP. The above argument yields the following
approximation for FT in term of the Lookahead value.
1
2 2
Msg
Msg T
T
E L
E L F
F L
 
 
  (8)
Substituting the value of (8) into (3), we get,
( )
1 1
2 2
S
S
LP
T T
Msg
Msg
T
Null E T
E
F F
 
   
 
   
   
 
   
 
(9)
Equation (9) can be generalized for O number of output
lines per LP when the numbers of null messages are generated
with a certain frequency of transmission. In other words, the
expected rate (i.e., FT) at which null messages may generate
per output line per LP can be roughly estimated as a percentage
of the Lookahead values. This expected rate per output line per
LP results (10) as follows:
( )
%
2 2
S
Msg S T
LP
Msg
T T
TO O
Null E T where F L
E
F F
   
 

   
 
 
   
 
   
  (10)
Equation (10) gives an estimated number of null messages
transmitted by single LP that has O number of output lines
where each line carry an equal percentage of the Lookahead
value in terms of a fixed frequency of transmission per output
Fig.1. Internal architecture of an LP
Fig.2. m number of logical processes with I number of input
queues and O number of output queues per LP.
line. In addition, if we assume that the system consists of m
number of total LPs where each LP has fixed number of output
lines, then (10) can be further extended for m number of LPs.
This generalization results (11) as follows:
( )
( )
( ) ( )
%
2 2
S
Msg T S T
m LP
Msg
T
T
Null E m O F T m O F
E
where F L
 
× ×
 
 
 

 
(11)
where the denominator of (11) (i.e.,
T
F
O) represents a
uniform rate of null message transmission per output line.
Based on (6), we can conclude that a non uniformity in null
message algorithm results non linear generation of null
messages. In other words, the approximation of null messages
can be well optimized when a non uniform transmission rate is
considered. Based on this argument, a mathematical expression
can be derived for O number of output lines where each line
may carry a different frequency of transmission.
( )
1 1
%
1
2 2
O O
Msg S
S
LP
i i
Msg
Ti Ti
Ti i
ET
Null T
E
F F
where F L
= =
   
 
   
 
 
   
 
   

∑ ∑
 
(12)
Furthermore, (12) can be further extended and generalized
for m number of LPs where each LP can have at most O
number of output lines. This generalization can be expressed in
(13).
( ) ( )
( )
( )
( )
( ) ( )
1 1 1 1
%
1
2
2
m O m O
Msg S Msg S
m LP T ki
k i k i T ki
T ki ki
Null E F T E T F
where F L
= = = =
 
 
 
 

∑ ∑
 
(13)
3.2. Optimization Via Variance for Null Message
Elimination in NMA
Also, in this scenario, it is essential to cancel out the
unnecessary generation of null messages. To consider and
analyze the effect of null message elimination on the
performance of PDES systems, we introduce variance as a
variable quantity. Variance represents the probability of
cancellation of unnecessary null messages. The value of
variance may exist between 0 and 1 (i.e., it can not be one,
since 1 represents that all generated null messages cancelled
with the maximum probability). It should also be subtracted
from 1, so that we can show that increase in variance causes a
decrease in the over all null messages where as a decrease in
variance causes an increase in null messages. If we consider
variance as 0, then it should give us the same results that we
could achieve with out using variance. In order to reflect the
variance of null message cancellation, we can rewrite (11) for
m number of LPs with the uniform distribution of null message
transmission per output line as follows:
( )
( )
( )
%
2 (1 )
(1 ) 0 1
2
S
Msg T
m LP
Msg
S T
T
T
Null E m O F E
O
T m where F L and
F
σ
σ σ
 
× −
 
 
 
 
×  ≤ <
 
 
 
(14)
where
σ
represents probability of null message cancellation.
The same concept of null message cancellation can be
implemented with a simulation model where the Lookahead
values are non-uniformly distributed among O number of
output lines. This leads us to the following modification in
(14):
( )
( ) ( )
( ) ( )
1 1 1 1
%
1
(1 ) (1 )
2 2
0 1
m O m O
Msg S
S
m LP
k i k i
Msg
T T
ki ki
Tki ki
ET
Null T
E
F F
where F L and
σ σ
σ
= = = =
 
   
− −
 
   
   
 ≤ <
∑ ∑
 
(15)
4. PERFORMANCE ANALYSIS OF THE PROPOSED
MATHEMATICAL MODEL
For the sake of performance analysis, we simulate 6 different
cases. The system is modeled in C++
4.1. CASE-I: Multiple Output Lines per LP
Using (4) [Null (LP) = Ts (O/L)], Fig.3 shows the null
message transmission with the following simulation
parameters: simulation time = 500 sec, L is uniformly
distributed per output line (O). The number of output line may
vary from 0 to 8 for all cases as show in Fig.3. Both numerical
and simulation results present a comparison of null message
transmission per LP versus multiple output lines.
4.2. CASE-II: Multiple LPs with Multiple Output Lines
per LP
In CASE-II, we assume that we have multiple LPs with O
output lines (fixed per LP). Let the output lines per LP is 4
with the simulation Time (Ts) of 500 sec. Using (5)
( )
S
Msg S
m LP
Msg
T
O O
Null E m T m
L E L
 
   
 
   
 
   
 
, Fig.4 shows the null
234567 8
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Output lines (O) Per LP
Null Message Transmission Per LP
Null(LP) with L=0.2
Null(LP) with L=0.4
Null(LP) with L=0.6
Null(LP) with L=0.7
Fig3. Multiple output lines per LP versus null message
transmission per LP
message transmission with the following simulation
parameters: simulation time = 500 sec, L is uniformly
distributed per output lines (O), the output lines are assumed to
be fixed for each LP (O = 4). The numbers of LPs are varied
from 1 to 10 as show in Fig.4.
4.3. CASE III: Multiple Output Lines per LP with Non-
Uniform Distribution of Lookahead
For this simulation, we assume that we have single LP that
has O number of output lines where each output line of an LP
can have different value of Lookahead (L). Using (6), Fig.5
shows the null message transmission with the following
simulation parameters: simulation time = 500 sec, L is non-
uniformly distributed per output lines (O). The numbers of
output lines are varied from 1 to 10 as show in Fig.5. Also, it
should be noted that the value of Lookahead is chosen
randomly within the range of 0 to 1 and assigned to each
output line at run time.
4.4. CASE-IV: Multiple LPs with Multiple Fixed Output
Lines where each Output line can have Different
Lookahead Value
For this simulation, we assume that we have multiple LPs
that can have fixed number of output lines where each line of
an LP can have different value of Lookahead (L). Using (7),
Fig.6 shows the null message transmission with the following
simulation parameters: simulation time = 500 sec, L is non-
uniformly distributed per output lines (O). The numbers of LPs
are varied from 1 to 20 as show in Fig.6. Also, it should be
noted that the value of m and O are both varying quantity for
this particular scenario.
5. CONCLUSION
We have proposed a mathematical model to predict the
optimum values of critical parameters that have great impact
on the performance of NMA. The proposed mathematical
model provides a quick and practical way for simulation
designers to predict whether a simulation model has potential
to perform well under NMA in a given simulation environment
by giving the approximate optimal values of the critical
parameters. We have experimentally verified that if critical
parameters, specifically the Lookahead value, are chosen
intelligently, we can limit the transmission of null messages
among the LPs.
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400
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Conference on Information and Emerging Technologies (ICIET-
2007), July 06-07, 2007, Karachi, Pakistan.
... Historically, two main methods have been introduced to deal with this problem: conservative [3] [4] and the optimistic synchronization algorithms (or Time Wrap) [5]. Two of the most common synchronization protocols for parallel simulation are the Chandy-Misra protocol [3] and the Time Warp protocol [5] (different approaches for parallel and discrete-event simulation and its applications are discussed elsewhere [6] [7] [8] [9] [10] [11] [12]). An introduction to the Chandy-Misra protocol and the Time Warp protocol can be found in [6] [13]. ...
... Historically, two main methods have been introduced to deal with this problem: conservative [3, 4] and the optimistic synchronization algorithms (or Time Wrap) [5]. Two of the most common synchronization protocols for parallel simulation are the Chandy-Misra protocol [3] and the Time Warp protocol [5] (different approaches for parallel and discrete-event simulation and its applications are discussed elsewhere6789101112). An introduction to the Chandy-Misra protocol and the Time Warp protocol can be found in [6, 13]. ...
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Time Wrap algorithm is a well-known mechanism of optimistic synchronization in a parallel discrete-event simulation (PDES) system. It offers a run time recovery mechanism that deals with the causality errors. For an efficient use of rollback, the global virtual time (GVT) computation is performed to reclaim the memory, commit the output, detect the termination, and handle the errors. This paper presents a new unacknowledged message list (UML) scheme for an efficient and accurate GVT computation. The proposed UML scheme is based on the assumption that certain variables are accessible by all processors. In addition to GVT computation, the proposed UML scheme provides an effective solution for both simultaneous reporting and transient message problems in the context of synchronous algorithm. To support the proposed UML approach, two algorithms are presented in details, with a proof of its correctness. Empirical evidence from an experimental study of the proposed UML scheme on PHOLD benchmark fully confirms the theoretical outcomes of this paper.
... Likewise, conservative approach has causality constraint which does not exist in the optimistic approach. An approach is different but goal of both approaches are same to simulate processes in a distributed environment [4]. ...
... Likewise, conservative approach has causality constraint which does not exist in the optimistic approach. An approach is different but goal of both approaches are same to simulate processes in a distributed environment [4]. Many algorithms are there in conservative algorithm for the distributed environment simulation. ...
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A conservative distributed simulation requires all logical processes (LPs) to follow the causality constraint requirement. This implies that all event-messages are processed in strictly timestamp order. Apart from the timestamp of each event generated by LPs, synchronization between all LPs is the second most important requirements. Finally, there must not be a deadlock in the distributed environment. A deadlock may occur when there is no events present in the queue of LP. In such case, to avoid deadlock, Chandy-Misra-Bryant presented an algorithm called Null Message Algorithm (NMA) [3]. These null messages are passed as an event-message to other LPs and it stored in one of queues of LPs. This null message indicates that till the time stamp of that null message, all other events in the queue which have lesser time stamp than null message’s time stamp are safe to process. It means that there won’t be anyarrival of any events from that logical process until current simulation time is equal to the time stamp of the null message. With the time stamp of the null message, a Lookahead value is added to the time stamp of that null message. This Lookahead value can be measure on certain kind of parameters such as delay to transmit a message, propagation delay, etc. therefore, calculating value of Lookahead is the most important part as Lookahead value affects the performance of the conservative distributed event simulation. Proper value of Lookahead can reduce the number of null messages which decreases thetraffic of the network. In this paper, we demonstrate some calculation on the Lookahead which shows the performance of the distributed event simulation
... Historically, two main methods have been introduced to deal with this problem: conservative [3,4] and the optimistic synchronization algorithms (or Time Wrap) [5]. Two of the most common synchronization protocols for parallel simulation are the Chandy-Misra protocol [3] and the Time Warp protocol [5] (different approaches for parallel and discrete-event simulation and its applications are discussed elsewhere [6][7][8][9][10][11][12]). An introduction to the Chandy-Misra protocol and the Time Warp protocol can be found in [6,13]. ...
... Other null message reduction algorithms that have been proposed use a generic mathematical model to approximate the optimal values of the parameters that are directly involved in the performance of a time management algorithm [33]. Thomas et al. [34] proposed another null message reduction algorithm based on grouping and status retrieval by determining an optimum value of the lookahead. ...
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This work attempts to provide insight into the problem of executing discrete event simulation in a distributed fashion. The article serves as the state of the art in Parallel Discrete-Event Simulation (PDES) by surveying existing algorithms and analyzing the merits and drawbacks of various techniques. We discuss the main characteristics of existing synchronization methods for parallel and distributed discrete event simulation. The two major categories of synchronization protocols, namely conservative and optimistic, are introduced and various approaches within each category are presented. We also present the latest efforts towards PDES on emerging platforms such as heterogeneous multicore processors, Web services, as well as Grid and Cloud environment.
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The field of parallel discrete event simulation is entering a period of self-assessment. Fifteen years of investigation has witnessed great strides in techniques for efficiently executing discrete event simulations on parallel and distributed machines. Still, the discrete event simulation community at large has failed to recognize many of these results. The central question is, why has this occurred ? One possible reason is an apparent disagreement in both the focus and objectives of the parallel discrete event simulation research community (primarily computer scientists) and the discrete event simulation community (a widely diverse group including, operations researchers, management scientists, mathematicians, and statisticians, as well as computer scientists). An examination of parallel discrete event simulation from a modeling methodological perspective illustrates some of these differences and reveals potentials for their resolution. 1 INTRODUCTION In a recent series of articles ...
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transmission during the G VT computation. Global virtual time (GVT) is used in parallel 1. Introduction discrete event simulations to reclaim memory, commit output, detect termination, and handle errors. The term distributed refers to distributing the Mattern's [1] has proposed GVT approximation with execution of a single run of a simulation program distributed termination detection algorithm. This across multiple processors [2]. One of the main algorithm works fine and gives optimal performance in problems associated with distributed simulation is the terms of accurate GVT computation at the expense of synchronization of distributed execution. If not slower execution rate. This slower execution rate properly handled, synchronization problems may results a high GVT latency. Due to the high GVT degrade the performance of a distributed simulation latency, the processors involve in communication environment [5]. This situation gets more severe when remain idle during that period of time. As a result, the the synchronization algorithm needs to run to perform overall throughput of a discrete event parallel a detailed logistics simulation in a distributed simulation system degrades significantly. Thus, the environment to simulate a huge amount of data as high GVT latency prevents the widespread use of this specified in "in press" [6]. algorithm in discrete event parallel simulation system. Event synchronization is an essential part of parallel However, if we could improve the latency of GVT simulation [2]. In general, synchronization protocols computation, most of the discrete event parallel can be categorized into two different families: simulation system would likely take advantage of this conservative and optimistic. Time Warp is an technique in terms of accurate GVT computation. In optimistic protocol for synchronizing parallel discrete this paper, we examine the potential use of tress and event simulations [3]. Global virtual time (GVT) is butterflies barriers with the Mattern's GVT structure used in the Time Warp synchronization mechanism to using a ring. Simulation results demonstrate that the reclaim memory, commit output, detect termination, use of tree barriers with the Mattern's GVT structure and handle errors. GVT can be considered as a global can significantly improve the latency time and thus function which is computed many times during the increase the overall throughput of the parallel course of a simulation. The time required to compute simulation system. The performance measure adopted the value of GVT may result in performance in this paper is the achievable latency for a fixed degradation due to a slower execution rate [4]. On the other hand, a small GVT latency (delay between its occurrence and detection) reduces the processor's idle Authorized licensed use limited to: University of Bridgeport. Downloaded on February 24,2010 at 13:16:22 EST from IEEE Xplore. Restrictions apply. time and thus improves the overall throughput of where as C2 guarantees that no message distributed simulation system. generated prior to the first cut is in transient. Mattem's [1] has proposed GVT approximation * For our analysis, we assume that tp is the with distributed termination detection algorithm. This required-time to send one message from one algorithm works fine and gives optimal performance in processor to its neighbor (note that this terms of accurate GVT computation at the expense of neighboring processor might be a child for C1 slower execution rate. This slower execution rate and a parent for C2). results a high GVT latency. Due to the high GVT * In addition to that, we also assume that both latency, the processors involve in communication rounds of message transmission are required
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The performance of a conservative time management algorithm in a distributed simulation system degrade s significantly if a large number of null messages are exchanged across the logical processes in order to avoid deadlock. This situation gets more severe when the exchange of null messages is increased due to the poor selection of key parameters such as lookahead values. However, with a mathematical model that can approximate the optimal values of parameters that are directly involved in the performance of a time management algorithm, we can limit the exchange of null messages. The reduction in the exchange of null messages greatly improves the performance of the time management algorithm by both minimizing the transmission overhead and maintaining a consistent parallelization. This paper presents a generic mathematical model that can be effectively used to evaluate the performance of a conservative distributed simulation system that uses null messages to avoid deadlock. Since the proposed mathematical model is generic, the performance of any conservative synchronization algorithm can be approximated. In addition, we develop a performance model that demonstrates that how a conservative distributed simulation system performs with the null message algorithm (NMA). The simulation results show that the performance of a conservative distributed system degrades if the NMA generates an excessive number of null messages due to the improper selection of parameters. In addition, the proposed mathematical model presents the critical role of lookahead which may increase or decrease the amount of null messages across the logical processes. Furthermore, the proposed mathematical model is not limited to NMA. It can also be used with any conservative synchronization algorithm to approximate the optimal values of parameters.
Discrete simulation is a widely used technique for system performance evaluation. The conventional approach to discrete simulation (e.g., GPSS, Simscript) does not attempt to exploit the parallelism typically available in queueing network models. In this paper, a distributed approach to discrete simulation is presented. It involves the decomposition of a simulation into components and the synchronization of these components by message passing. This approach can result in the speedup of the total time to complete a given simulation if a network of processors is available. The architecture of a microcomputer network suitable for distributed simulation is described and some results concerning the distributed approach are presented.
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The prevention of deadlock in certain types of distributed simulation systems requires special synchronization protocols. These protocols often create an excessive amount of performance-degrading communication; yet a protocol with the minimum amount of communication may not lead to the fastest network finishing time. We propose a protocol that attempts to balance the network's need for auxiliary synchronization information with the cost of providing that information. Using an empirical study, we demonstrate the efficiency of this protocol. Also, we show that the synchronization requirements at different interfaces may vary; an integral part of our proposal assigns a protocol to an interface according to the interface's synchronization needs.
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This paper explores several variants of the Chandy-Misra Null Message algorithm for distributed simulation. The Chandy-Misra algorithm is one of a class of “conservative” algorithms that maintains the correct order of simulation throughout the execution of the model by means of constraints on simulation time advance. The algorithms developed in this paper incorporate an “event-oriented” view of the physical process and message-passing. The effects of the computational workload to compute each event is related to speedup attained over an equivalent sequential simulation. The effects of network topology are investigated, and performance is evaluated for the variants on transmission of null messages. The performance analysis is supported with empirical results based on an implementation of the algorithm on an Intel iPSC 32-node hypercube multiprocessor. Results show that speedups over sequential simulation of greater than N, using N processors, can be achieved in some circumstances.
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Originating from basic research conducted in the 1970's and 1980's, the parallel and distributed simulation field has matured over the last few decades. Today, operational systems have been fielded for applications such as military training, analysis of communication networks, and air traffic control systems, to mention a few. The article gives an overview of technologies to distribute the execution of simulation programs over multiple computer systems. Particular emphasis is placed on synchronization (also called time management) algorithms as well as data distribution techniques
Conference Paper
Most work on parallel discrete event simulation has been based on a distributed model of computation in which processes can only communicate through message passing. Here we study parallel discrete event simulation under a common memory model of computation. An algorithm for parallel discrete event simulation is developed based on the assumption that every process has direct access to the state of any other process. The objective is to avoid the high overhead associated with null messages and request messages in distributed algorithms. This algorithm is then compared to distributed synchronization algorithms.