Performance Evaluation of a Dead Reckoning mechanism Corentin Durbach PRiSM - UVSQ 45, Avenue des Etats-Unis 78000 Versailles - FRANCE
[email protected]
Abstract Dead Reckoning mechanism allows to reduce the network bandwidth utilization considerably. As available bandwith is the key problem for large DIS, we expect that a Dead Reckoning mechanism will allow to increase the number of entities involved in a DIS exercise. In this paper we model a Dead Reckoning mechanism and we present an evaluation of its performance. Such a mechanism reduces the number of PDU exchanged during the simulation. But it also completly changes the nature of the stochastic process which models the arrivals of PDUs. Indeed, it adds some kind of sporadicity. We present some measurements on a DIS simulator which exhibits such a behaviour. Then we investigate the effects of such a mechanim in terms of response time and number of allowed entities using a simulation tool. Some extensions towards the numerical resolution of a large Markov chain associated to the problem are finally presented. Keywords : DIS, Dead Reckoning, Performance Evaluation, Simulation, Markov Chain, HLA.
This work has been partially supported by a grant from Direc-
tion G´en´erale de l’Armement
Jean-Michel Fourneau PRiSM - UVSQ 45, Avenue des Etats-Unis 78000 Versailles - FRANCE
[email protected]
1. Introduction The aim of Dead Reckoning mechanism is to reduce the utilization of the network bandwidth during a DIS exercise. One of the objectives of DIS is to handle a very large number of active entities. It is generally acknowledged that such exercices will generate a huge amount of network traffic. Even if some new network technologies such as asynchronous transfer mode (ATM) or group multicast will provide a high bandwith, some softwares are still necessary to reduce the number of PDUs exchanged during the simulation. If the PDUs emission is carried out at each movement of an entity, the frequency of that emission would be the same as that of visual implementation, i.e. 10 Hz for the ground objects and 30 Hz for the flying objects. For DIS simulations, the emission is performed in Broadcast mode, hence a O(n2) traffic for a complete exchange of positions for the whole set of entities. The bandwidth would be quickly saturated as the number of active entities becomes important for large scale simulations. Using a Dead Reckoning mechanism allows to considerably reduce the stream of data transmitted by the network. The principle of such a mechanism is to transmit PDUs (threshold in distance, threshold in orientation, ...), while limiting the emission rate, and the PDUs are transmitted only if we exceed that threshold. For instance, when a tank moves about on a road, its position is supposed to be almost linear ; thus one does not need to transmit its position continually, one transmits it only if the extrapolation mechanism detects that
associated to our model.
the appointed threshold is exceeded (like a change in orientation). For a plane, its trajectory is not as easy to predict. The threshold is rapidly exceeded and the PDUs emissions will then be performed with a higher frequency. One also defines a maximal time between two emissions (generally 5 seconds) in which we send the position of the entity (or other pieces of information ) in a determinist way, which permits a minimal updating for the other entities.
2. A Model for the PDUs generation We have used several techniques to analyze the performance of Dead Reckoning mechanism. First we have performed some measurements on a testbed to find a statistical model of the interarrival of PDUs on the network. We have also performed the analysis of the data to get the parameters of the model. Assuming some kind of independence and a doubly stochastic arrival process, this models will lead to a continuous time Markov chain which represents the network. As this chain has a large state-space, we do not expect to solve it for a large number of entities. Thus we have designed a simulator (in Qnap II [13]) which takes into account the characteristics of the generation process. This model is more accurate that the ones based on Poisson arrivals of PDUs as it correctly represents the sporadicity of the generation due to the mechanism. The sporadicity implies some variability of the process [6] and this explains why the performances may decrease so quickly. It suggests also some ideas to improve the performance of DIS which rely on some policing techniques designed for high speed networks.
Various extrapolation mechanisms adapted to the existing entities allow to reduce the PDUs frequency, but the non-predictive characteristic of a trajectory or the change from a phase of simple movement to a phase of engagement does not allow to predict whether the appointed threshold will be exceeded. It is principally because of that type of change that the very nature of the PDUs emissions is stochastic. Of course, delay due to the stack of protocols is also at random. Thus, the network as well as the latency period induced by additional activity cannot be defined systematically for a predefined type of exercise. The purpose of this study is to analyze the influence of Dead Reckoning on the network and on the response time. One will here be concerned only with the network, considering it to be the main bottleneck of the DIS system. It is interesting to define the maximal number of entities which can transmit PDUs simultaneously without deteriorating the overall performances of the simulation. Indeed, if one wants to carry out simulations at a very large scale, it is important to define the capacities of the network one will use according to the needs of a simulation exercise. In order to implement this, the idea is to get back the traces of the PDUs emissions through the network in order to define a model, and then to perform again scenarios thanks to modeling tools while modifying a certain number of parameters (number of entities, frequency of each entity, processing time of the network, etc. ...).
2.1. Traffic observation The first step consists in doing some measurements on a real system (a testbed of four workstations using DIS 2.0.3) to get some real data and observe the statistical characteristics of the traffic. To implement the analysis of the PDUs traffic on the network, one must proceed in the following steps :
perform a simulation exercise on a local network set a logger on the network in order to store a trace of the PDUs transmitted by different entities into a file. measure the time difference between two interarrivals of PDUs transmitted by a group of entities or by an entity
The following Section presents the analysis of Dead Reckoning and the model we propose ; Section 3 lays out the different goals we aimed at ; Section 4 provides the experimentations. In Section 5, we present the conclusions and give some insights on some forhcoming work on the numerical analysis of the Markov chain
draw an histogram of the interarrival intervals to get some insight of the distribution. study the distribution using statistical techniques, tests of adequation or filters. 2
2.2. Analysis per entity
: 4% of the sent PDUs are transmitted every 4.4 seconds, the other PDUs are transmitted on average every 0.2 second and 10 % every 0.1 second.
The analysis per entity is achieved by taking only the interarrival periods of the PDUs transmitted by a single entity. Consequently, we only consider the evolution of a single entity in the course of the simulation. The folowing example presents the displacement of an entity on a winding route. The Dead Reckoning mechanism will permit to reduce the PDU emissions in the so-called “linear” parts. The rest of the time, the Dead Reckoning do not intervene, and the PDU emissions are sent at the normal frequency. The following figure represents the sample-path of the interarrival times between two successive PDUs transmitted by an entity. It is worthy to remark that two regions for the interarrivals exist : the one with an interarrival time of 4.5 seconds, and the one with a very short delay of a few milliseconds. These 2 types of interarrivals show the transition from a stage where the emissions are reduced (Dead Reckoning acts strongly) to a stage where the emissions are sent whitout filtering.
12 ’class_ind.txt’
10
8
6
4
2
0 0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Figure 2. Histogram of the interarrivals for a single entity
4.5
Two important points have to be noted : the high variability of the interarrival times and the correlation between two successive delays : such a distribution is usually characterized as bursty.
’indiv.txt’ 4
3.5
3
2.5
2.3. Analysis per group of entities
2
1.5
The analysis is identical to the previous one, except that we take a group of entities (same site, same application, etc. ...), or all the entities which are active during the simulation. The analysis per group of entities shows a behaviour quite similar to the one of an isolate entity. Indeed, if one assumes that all the entities use the same Dead Reckoning mechanism with the same parameters, the overall behaviour of that mechanism will have the same influence on the frequency of the PDUs for each one of the entities. This is the case of an homogeneous set of entities. If the parameters of the mechanism are different we may obtain a non homogeneous set with several spikes in the histogram. These values are the various parameters of the mechanism. We may assume, for instance, that the parameter for a plane is quite different from the parameter for a tank.
1
0.5
0 0
500
1000
1500
2000
2500
3000
Figure 1. sample-path of interarrival times of PDUs
The second graph shows an histogram of the distribution of the interarrival times of an entity. On the Y-axis, there is the delay between two successive emissions : the maximum time between two interarrivals is of 4.4 seconds, and the minimum time 0.1 second ; on the X-axis, there is the number of times when one transmits the PDUs at a particular frequency during the simulation. The values are expressed in percentage 3
14
with a larger Markov chain for the phasis.
’class_grp.txt’ 12
10
8
6
4
2
0 0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Figure 3. Histogram of the interarrivals for a group of entities
βi
Poisson reflect
Deterministic
λ
QUICK
2.4. Probabilistic model These analyses, presented in previous paragraph, are to be used as a support to define a model in order to predict the reponse time of the network. The two regions observed in the distribution of the PDU interarrivals suggests a doubly stochastic process (i.e. a process whose parameters and type are modulated by an auxiliary Markov process). To keep the model as simplest as possible, it is sufficient to use a two-state Markov process to represent the two activity modes of the entities. One state is denoted as the ”quick state” and the other one as the ”slow state”. This chain is denoted as the phasis of the arrival process. The real nature of this arrival process varies according to the state of the phasis. If the phasis is in ”quick state”, then the arrivals follow a Poisson process of unknown parameter . On the contrary, when the arrivals are deterministic (in the example previously suggested, the deterministic arrivals are sent with a delay of 4.5 ms) then the phasis is in ”slow state”. Such a process is a generalization of Markov modulated Poisson process (MMPP, see [6]). Indeed, in an MMPP, parameters change but the arrivals allways follow Poisson processes. As one does not have any statistical information about the distribution of the time spent in these two states of activity, it is assumed that their distribution is exponential. More complex distributions may be used
SLOW
αi
Figure 4. Markov representation of the change of phase
So each entity is associated to a two-state phasis. If we consider n active entities, the set of entities is represented by a 2n phasis which is built on the cartesian product of the elementary phasis. However some of these states are not reachable due to some synchronous transitions of the phasis. For instance, if two planes begin to fight, they switch at almost the same time from ”slow state” to ”quick state”, if we assume that the two planes have the same kind of equipment. In pessimistic cases, all the entities switch at the same time. This is certainly the worst case as this instant has to be associated with the quickest entity. But in this case, the state space with of the phasis collapses into two states, which is certainly simpler to analyze. This study focuses on the simulation aspect of this model for various kind of configurations. We suggest in the conclusions how some simple configurations may be solved numerically using a Markov chains solver. We use a simulation program written in Simu4
3. Experimentation
log/QNAP II langage ([13], [1]). This langage is based on queues and customers. Thus all the objects formerly defined are translated into queues and customers. We describe the interarrival process by the following three queues : a source of customers and two queues to represent the state of the entity. The network is represented by a queue and the PDUs emissions are represented by customers transmitted by sources. The size of the queue is considered to be infinite because the loss rate, at the application level, is supposed to be negligible. The service is supposed to be deterministic (we assume that PDUs have a constant size of 144 bytes). We also assume that the network is an Ethernet LAN at 10Mbps. The i (i 2 [1::n]) represents the arrival process of the PDUs transmitted by the i-th entity on the network.
3.1. Purpose To begin with, we must validate our model in order to be able to simulate a large number of entities and to draw conclusions on the throughput of the network. We have performed analyses on a dozen of entities in order to adjust the parameters ( ; ; ; :::), so that our model corresponds at best to our real simulator. One of the important constraints which is to be respected for a DIS exercise is the response time of the network. A PDU must reach its destination within a bounded delay of 100 ms. If the threshold is exceeded, one can no longer hold the real time constraint. The purpose of our work is to evaluate the real throughput for the PDUs due to the contention of the network. This contention is higly dependant on the stochastic properties of the arrivals. Our simulation tool allows to get the distribution of the response time of the network during a DIS exercise with a fixed number n of entities. We also perform simulations for several values of n and different mixtures of the set of entities to study the evolution of this distribution.
The two stations QUICK and SLOW represent the two possible states of an entity, namely the ”slow activity state” and the ”quick activity state”. A single customer moves into those two queues, its entry into the other queue represents the change of phase. Each queue has a Poisson service time ( i for the QUICK and i for the SLOW). If the customer is in the QUICK queue, the i process is Poisson of average di ; otherwise the customer is in the SLOW queue and the process is deterministic.
3.2. Results
Modulated Process / M / 1 αi
QUICK
quick
λi = βi
{
cste or expo( δ i)
SLOW
slow
λ1 µ
...
network
λn
OUT
Network
Figure 5. modeling of the network
5
The following graph, presents the average response time (in ms) of the network versus the ratio =( + ) for three values of the number of entities (10 sources, 50 sources, 100 sources). This ratio is associated to the burstiness of the arrivals as it governs the amount of time spent in the ”quick activity state”. One notices the impact of the change of phase on the network response time. The next figure presents the distribution of the response time. This distribution is very closed to the average when the number of entities is small (i.e. the load is light). But when the number of entities increases, the distribution has a larger standard deviation (the load is heavy and more delays are experienced by PDUs). Then figure 8 shows the influence of the number of entities on the network average response time for three fixed values of . It is worthy to remark that the increase of the response time is non linear. Until 300 entities, the average response time is smaller than 100 ms, and after that limit, its evolution
250
1 ’entite.txt’ ’entite.txt’ ’entite.txt’
’100_entities’ ’200_entities’ ’300_entities’ ’350_entities’ ’400_entities’ ’450_entities’
0.9
200
0.8 0.7
150
0.6 0.5
100
0.4 0.3
50
0.2 0.1
0
0 0
100
200
300
400
500
600
0
Figure 6. evolution of the response time according to the number of sources (homogenous)
10
20
30
40
50
60
70
80
90
100
110
Figure 7. Distribution of the response time in ms
we may adress in the future. is almost exponential. We obtain similar results for the 90%-percentile of the distribution.
Another remark based on the measurement of traffic and its implication on the response time is the need of a smoothed traffic such as the policies which are proposed for high speed networks. Dead Reckoning as well as Filtering decrease the bandwith utilization but, the full benefice of those mechanisms may not be obtained until we may more efficiently multiplex the PDUs of the active entities.
4. Conclusion This work has permitted to define a model for the performance evaluation of Dead Reckoning mechanism. One has been able to obtain, by simulation, a boundary for the number of entities which may be active during an exercise with a guaranty on the 95% percentile of the response time.
References
It may be also possible to solve a Markov chain associated to the network and the n entities. The state space of the phasis may be as large as 2n and the state of the queue may be potentially infinite (even if we may perform some truncations). Thus, numerical techniques, such as matrix geometric technique created by Neuts, may be difficult to apply. The first step consists in slightly changing the model of the process. Indeed the superposition of Poisson processes and deterministic arrivals is difficult due to the different nature of the times which are considered. It is more convenient to use Poisson processes and anoter process based on the combining of exponentials. As the interarrival times are almost deterministic in a region, we may model those arrivals by an Erlang distribution with k stages. This leads to an interesting Markovian modeling that
[1] M. Badel, D. Duong, and S. Eyraud. The new simulation facilities in qnap. Proceeding of the 1991 European Simulation Sympoisum, 1991. [2] C. Bouwens and R. Matusof. Predicting network performance in heterogenous, multi-fidelity, simulation networks. 10th Workshop for the Interopreability of Defense Simulation, 1994. [3] M. Brig. Dis and simnet network log file analysis. 14th DIS Workshop, pages 96–14–034, 1996. [4] K. Doris and M. Loper. Dis network traffic analysis estimation techniques. 10th Workshop for the Interopreability of Defense Simulation, pages 887–890, 1994. [5] N. Durlach and J. Morrison. The vr-link, networked virtual environment software infrastructure. 10th Workshop for the Interopreability of Defense Simulation, 1994.
6
100 ’100_entites’ ’50_entites’ ’10_entites’ 80
60
40
20
0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figure 8. response time in ms according to
+
140 ’10_entities_nh’ ’50_entities_nh’ ’100_entities_nh’ 120
[6] W. Fischer and K. Meier Hellsterm. The markovmodulated poisson process (mmpp) cookbook. Performance Evaluation, 18:149–171, 1992. [7] B. Kelly and S. Aggarwal. A framework for a fidelity based agent architecture for dis. 14th DIS Workshop, pages 96–14–077, 1996. [8] R. Long and R. Anschuetz. Performance limitations of the dis interface. 10th Workshop for the Interopreability of Defense Simulation, 1994. [9] M. Loper and L. Bassiouni. Evaluating the overhead of osi stacks in interoperable dis networks. Technical Report, 1995. [10] M. Pullen and D. Wood. Networking technology and dis. Proceeding of the IEEE, 83(8), August 1995. [11] S. Rak. Evaluation of grid-based relevance filtering for multicasting group assignement. 14th DIS Workshop, pages 96–14–106, 1996. [12] U. Vemulapati, R. Uschold, and S. Smith. Application level hardware filtering for dis. 14th DIS Workshop, pages 96–14–005, 1996. [13] M. Veran and D. Potier. New user’s introduction to qnap2. INRIA Technical Report, 40, 1984.
100
80
60
40
20
0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Figure 9. evolution of the response time according to the number of sources
7
1
