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6 S UB i ∑ = P LI / LI . (16) i p∈K n( i) So, a component i can complete by T LB and generate tasks at a constant interval of T LB /L i from t=S i UB when it receives tasks at a constant interval of T LB /L i from t=0. Now, consider component i’s successor s which has only one predecessor. As the successor receives tasks at a constant interval of T LB /L s from t=S i UB or more preferably, it can complete by S i UB +T LB . So, a component e∈E (with no successor) can receive tasks at a constant interval of T LB /L e from maximal task traveling time to the component of: Max j∈S e ∑ i∈ j S p UB i i (17) (note that a path j does not include component e) or more preferably so that its completion time T e is bounded as: T e ≤ T LB + Max j∈S e ∑ i∈ j S UB i . (18) And, the upper bound of T is the maximal of the bounds. Though we formulated the upper bound performance without considering stress environments, one can easily modify it so that the upper bound performance can reflect the stress environments (if each ω n s is identifiable or assumable). The adequacy criterion is defined as the ratio between T LB and T UB as in (19). When the criterion is close to one, a network can achieve the lower bound performance using the proportion allocation policy. Typically, the criterion converges to one as each L i increases. However, as the criterion approaches zero, the policy become more and more inadequate. The example network in Fig. 1 is quite adequate because the network’s adequacy is 0.99 (300/303). LB T Adequacy = (19) UB T So far, we assumed a hypothetical weighted round-robin server which is difficult to realize in practice. But, our arguments do not seem to be invalid because they are based on worst-case analysis and quantum size is relatively infinitesimal compared to working horizon in reality. D. Resource control mechanism Once a network has an appropriate adequacy over a certain level (depending on the nature of the network), the proportional allocation is deployed periodically under MPC framework. Consider current time as t. To update load index as the system moves on, we slightly modify it to represent total CPU time for the remaining tasks as: LI ( t ) = R ( t ) + L ( t ) P , (20) i i in which R i (t) denotes remaining CPU time for a task in process and L i (t) the number of remaining tasks excluding a task in process. After identifying initial number of tasks L i (0)=L i , each component updates it by counting down as they process tasks. Periodically, a resource manager of each node collects current LI i (t)s from residing components and allocates resource proportional to the indices as in (21). As the resource allocation policy is purely localized there is no need for synchronization between nodes. The designed resource control mechanism is scalable as each node can make decisions independent of others while requiring almost no computation. w i i ( t) ωn( i) ∑ LI p ( t) p∈K n( i) i i LI ( t) = (21) VI. EMPIRICAL RESULTS We ran several experiments using discrete-event simulation to validate the designed resource control mechanism. A. Experimental design The experimental network is composed of eight components in four nodes as in Fig. 3. Two components are sharing a resource in N 3 and four components in N 4 . Also, ω n is 1 for all n∈N and CPU is allocated using a weighted round-robin scheduling in which CPU time received by each component in a round is equal to its assigned weight. N 1 N 2 A 1 N 3 A 3 A 4 N 4 A 5 A 6 A 7 A 8 Fig. 3. Experimental network configuration. The network is composed of eight components in four nodes and the performance can depend on the resource allocation of nodes N 3 and N 4 . We set up ten different experimental conditions as shown in Table I. We vary the number of root tasks rt i and CPU time per task P i , and the distribution of P i can be deterministic or exponentially distributed. While using stochastic distribution we repeat 5 experiments. We use three different resource control policies for each experimental condition. Table II shows these control policies. In round-robin allocation policy (RR) the components in each node are assigned equal weights over time. PA-O and PA-C use the proportional allocation policy in open-loop and closed-loop A 2
7 respectively. In PA-O resources are allocated only at t=0 and kept over time while in PA-C periodically (every 100 time units). PA-C is the resource control mechanism we have designed. B. Results TABLE I EXPERIMENTAL CONDITIONS Condition Distribution of P i rt i P i Con1-1 Deterministic [000 000 000 000 [04 12 04 08 Con1-2 Exponential 200 200 200 200] 02 02 02 02] Con2-1 Deterministic [100 100 100 100 [04 12 04 10 Con2-2 Exponential 200 200 200 200] 02 02 06 06] Con3-1 Deterministic [100 100 100 100 [04 12 04 10 Con3-2 Exponential 200 200 200 100] 02 02 20 10] Con4-1 Deterministic [100 100 100 100 [04 12 04 08 Con4-2 Exponential 200 200 200 200] 02 02 10 02] Con5-1 Deterministic [100 100 200 200 [04 10 04 08 Con5-2 Exponential 200 200 200 200] 02 02 02 02] TABLE II CONTROL POLICIES FOR EXPERIMENTATION Control policy Description RR Round-Robin allocation PA-O Proportional allocation - Open loop PA-C Proportional allocation - Closed loop Numerical results from the experimentation are shown in Table III. Lower and upper bounds are calculated for each experimental condition. The network adequacy of each condition is close to one and the proportional allocation policy can be used effectively for all the conditions. Proportional allocation policies (PA-O and PA-C) shows significant advantages compared to round-robin allocation in all the different conditions. The completion time T under proportional allocation is bounded to T UB and close to T LB in all deterministic conditions (note that the performance of PA-O and PA-C is the same in deterministic environments), supporting the effectiveness of the resource allocation policy. Though T UB does not work accurately in stochastic environments, the performance improves close to T LB when the proportional allocation is implemented in closed-loop. The periodic design process alleviates the impacts of stochasticity. So, we can conclude that the designed control mechanism can be effectively used even in stochastic environments for the networks with high adequacy. The performance differences can be reasoned from resource utilization as discussed earlier. A node with maximal total CPU time needs to utilize its resource almost fully to achieve a performance close to T LB . For example, N 2 is such a node in Con1-1 (deterministic) and Con1-2 (stochastic). Resource utilization profiles of N 2 are shown in Fig. 4 for Con1-1 and Fig. 5 for Con1-2, in which a data point corresponds to the amount of utilized resource during a control period (100 time units). In deterministic environment (Con1-1), N 2 utilizes its resource almost fully under both proportional allocation Utilization (%) 100 80 60 40 20 PA-O RR PA-C 0 0 1000 2000 3000 4000 5000 6000 Fig. 4. Resource utilization of N 2 in Con1-1. In a deterministic environment, N 2 utilizes its resource almost fully under both proportional allocation policies (PA-O, PA-C) while underutilizing in initial stage under round-robin allocation policy (RR). Utilization (%) 100 80 60 40 20 PA-O RR Time 0 0 1000 2000 3000 4000 5000 6000 Fig. 5. Resource utilization of N 2 in Con1-2. In a stochastic environment, N 2 utilizes its resource more under proportional allocation policies (PA-O, PA-C) compared to round-robin allocation policy (RR), and resource utilization under closed-loop policy (PA-C) is larger than under open-loop policy (PA-O). Time PA-C TABLE III EXPERIMENTAL RESULTS Control policy RR PA-O PA-C T LB T UB Adequacy T T LB /T T T LB /T T T LB /T Con1-1 4800 4820 0.996 5619 0.854 4820 0.996 4820 0.996 Con1-2 4800 4820 0.996 5618 0.854 5021 0.956 4939 0.972 Con2-1 7200 7230 0.996 7612 0.946 7200 1.000 7200 1.000 Con2-2 7200 7230 0.996 7679 0.938 7323 0.983 7252 0.993 Con3-1 6000 6073 0.988 6412 0.936 6012 0.998 6012 0.998 Con3-2 6000 6073 0.988 6408 0.936 6193 0.969 6013 0.998 Con4-1 7200 7228 0.996 7200 1.000 7200 1.000 7200 1.000 Con4-2 7200 7228 0.996 7231 0.996 7109 1.013 7169 1.004 Con5-1 7200 7220 0.997 7810 0.922 7210 0.999 7210 0.999 Con5-2 7200 7220 0.997 7979 0.902 7351 0.979 7319 0.984
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Ultra*Log PSU/IAI Final Report for
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Contents Contents .................
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Executive Summary Ultra*Log is a De
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2.3 Gnanasambandam, N., Lee, S., Ku
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6 Characterization and analysis of
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timizing simultaneously the link de
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where ∆ 1 (j) ≥ 0 and ∆ 2 (i,
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Table 2. GA Results Agent N A D max
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connected component, in which a pat
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Random Small-world Scale-free with
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Growth mechanisms Start with a smal
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Table 2. The proposed network’s c
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© © ¤ ¢ ¨ ¤ £ ¦ ¨ © §
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DMAS Controller. The functional uni
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1000 500 0 -500 -1000 0.2 0.4 0.6 0
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tems. Proceedings of the Second Joi
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Proceedings of the 1st Open Cougaar
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1 SITUATION IDENTIFICATION USING DY
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3 3.2 Behavior In SSC society an ag
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5 All the behavior parameters may n
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Estimating Global Stress Environmen
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chaotic deterministic time series.
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100% 1 95% 2 14 15 64% TAO 4 64% 62
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interactions as a dynamical system
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ehavior states under varying system
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Page 118 and 119: component is a member of one of the
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Page 122 and 123: limit of large number of tasks. If
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Understanding Agent Societies Using
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• For tasks, the UID of the direc
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for tracking the dependencies betwe
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within the monitored enclave. With
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Figure 1. Agent Hierarchy in CPE So
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Figure 3. The World Model CPY Agent
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Table 2. TechSpecs: Infrastructure
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terms of the average waiting times
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Acknowledgements The work described
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key realization to tackle this prob
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are or ignored perturbations. The e
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sustained oscillations. If the inst
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solved by biological systems for li
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non-linear and non-stationarity. Ne
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D k : Outflow from high priority qu
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the system starts to perform self-s
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sustained in a supply chain. Resour
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which are necessary to make good mo
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focusing on the computational compl
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line of research that deals with ne
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ealizable. But the inherent complex
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Min, H. and Zhou, G., 2002, Supply
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In the rest of this paper we report
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shows relatively irregular behavior
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