COORDINATION OF PLANNING AND SCHEDULINGTECHNIQUES FOR A DISTRIBUTED, MULTI-LEVEL,

MULTI-AGENT SYSTEM

John S. Kinnebrew, Daniel L. C. Mack, Gautam Biswas, Douglas C. SchmidtDepartment of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN 37203, USA

john.s.kinnebrew@vanderbilt.edu

Keywords: Planning and Scheduling, Agent Cooperation and Coordination.

Abstract: Planning and scheduling for agents operating in heterogeneous, multi-agent environments is governed by thenature of the environment and the interactions between agents. Significant efficiency and capability gains canbe attained by employing planning and scheduling mechanisms that are tailored to particular agent roles. Thispaper presents such a framework for a global sensor web that operates as a two-level hierarchy, where themission level coordinates complex tasks globally and the resource level coordinates the operation of subtaskson individual sensor networks. We describe important challenges in coordinating among agents employingtwo different planning and scheduling methods and develop a coordination solution for this framework. Ex-perimental results validate the benefits of employing guided, context-sensitive coordination of planning andscheduling in such sensor web systems.

1 INTRODUCTION

In large-scale, distributed, multi-agent systems(MAS) that span multiple domains of agent operation,choosing a single planning and scheduling mecha-nism for all agents may be inefficient and impractical.For example, NASA’s Earth Science Vision calls forthe development of a global sensor web that providescoordinated access to sensor network resources for re-search and resolution of Earth science issues (Hilde-brand et al., 2004). This global sensor web must se-lect and coordinate an appropriate subset of hetero-geneous, distributed sensors and computational re-sources for user tasks that often require collaborationamong multiple constituent sensor networks. Com-plex task execution with resource constraints and timedeadlines presents planning, scheduling, and coordi-nation issues at multiple levels of the sensor web.

Our Multi-agent Architecture for Coordinated Re-sponsive Observations (MACRO) platform providesa powerful computational infrastructure for deploy-ing, configuring, and operating large sensor webs withmany constituent sensor networks (Suri et al., 2007).MACRO is structured as a two-level agent hierar-chy: (1) the mission level, where global coordina-

tion across sensor networks is achieved and planningand scheduling is handled at an appropriate level ofabstraction to avoid computational intractability, and(2) the resource level, where operations within a lo-cal sensor network are coordinated and controlled us-ing planning and scheduling methods that operate indynamic, uncertain and resource constrained environ-ments. Therefore agents at these different levels ofthe system operate in different contexts imply differ-ent planning and scheduling requirements.

MACRO achieves efficient and effective au-tonomous planning by employing hierarchical tasknetwork planning with distributed scheduling at themission level and decision theoretic planning with re-source constraint propagation scheduling at the re-source level. Developing such an agent architec-ture, however, also presents challenges in coordinat-ing among the agents . In particular, employing differ-ent planning and scheduling mechanisms at the mis-sion and resource levels requires an appropriate trans-lation of the task, plan, and schedule representationsbetween levels. It also requires a coordination mech-anism for deciding when to exchange information be-tween levels during plan execution.

The remainder of the paper is organized as fol-

lows: Section 2 outlines the key capabilities pro-vided by the MACRO agent framework; Section 3summarizes the planning and scheduling coordinationchallenges and the solutions we developed for thispaper; Section 4 evaluates experimental results thatshow the reduction in communication and computa-tion achieved by using MACRO’s guided, context-sensitive coordination mechanism for planning andscheduling; Section 5 compares our work with relatedresearch; and Section 6 presents concluding remarks.

2 OVERVIEW OF MACRO

To provide global coordination of the sensor web, theMACRO mission level is comprised of broker agents,user agents, and mission agents. Broker agents act asthe intelligent system infrastructure, providing match-maker services, aggregating relevant domain informa-tion, tracking system performance, and mediating al-location negotiations (Kinnebrew, 2009). User agentsgenerate the high-level tasks and are typically inter-faces to mission scientists and wrappers for legacysystems (e.g. weather modeling applications) that canrequest execution of sensor web tasks. Each missionagent represents an independent sensor network andachieves its allocated tasks with the resources avail-able in its sensor network.

As the representative of an entire sensor network,a mission agent straddles the boundary between themission and resource levels. At the resource level,mission agents divide tasks among the exec agents,each of which controls a set of computational/sensorresources within a sensor network and is supported byadditional domain-specific agents. An exec agent alsoemploys services for planning, scheduling, allocation,and resource management of the hardware under itscontrol. These services are shared with any support-ing agents under its direction, providing a centralizedcontrol and environmental awareness for its set of re-sources.

2.1 MACRO Mission Level

At the mission level of a sensor web MAS, usertasks and scheduled plans spanning multiple sensornetworks have a high degree of complexity. Hi-erarchical analysis helps deal with this complexity,both for problem/task representation by domain ex-perts and for coordinated planning and schedulingamong multiple agents. MACRO combines the OGCSensorML (Botts et al., 2007) representation of sen-sors and data processing with the Task Analysis, En-vironment Modeling, and Simulation TÆMS hierar-

chically decomposable task representation (Horlinget al., 1999) for multi-agent planning and schedul-ing. This combination provides standardized descrip-tions of task/subtask requirements and effects acrosssensor networks. The TÆMS representation also al-lows the specification of discrete probability distribu-tions for task/subtask characteristics including poten-tial outcome quality and duration (Lesser et al., 2004).

To coordinate and schedule TÆMS tasks acrosssensor networks, MACRO mission agents employ theGeneralized Partial Global Planning (GPGP) (Lesseret al., 2004) coordination mechanism, which worksin conjunction with a planning and scheduling mech-anism that can generate an appropriate task decompo-sition and schedule from a TÆMS task tree. For thispurpose, MACRO mission agents employ Design-To-Criteria (DTC) (Wagner and Lesser, 2001) plan-ning/scheduling, which has successfully been used inconjunction with GPGP coordination (Lesser et al.,2004). DTC scheduling is a soft real-time, heuristicapproach to solving the combinatorial problem of op-timally decomposing and scheduling a TÆMS task.DTC is particularly suited to the MACRO mission-level because it can optimize plans and schedulesbased on user-provided criteria, such as minimizingexecution time or maximizing expected quality.

2.2 MACRO Resource Level

Exec agents use the Spreading Activation PartialOrder Planner (SA-POP) (Kinnebrew et al., 2007),which generates high utility, scheduled, partial or-der plans that respect local resource constraints. SA-POP allows the exec agents to use their limited com-putational resources to maximize expected utility forachieving local goals in the dynamic, uncertain en-vironments at the resource level. Moreover, SA-POP provides incremental re-planning/re-schedulingthat can quickly revise scheduled plans during ex-ecution and prevent more expensive re-planning/re-scheduling at the mission level. In conjunction withSA-POP, exec agents also employ the Resource Allo-cation and Control Engine (RACE) (Shankaran et al.,2007) for resource allocation and management tomeet scheduled deadlines and required quality of ser-vice (QoS) parameters for deployed applications andhardware-based actions.

First-principles planning (Blum and Furst, 1997)and scheduling with SA-POP requires a set of goalconditions that correspond to the desired outcome.These goal conditions are specified as desired en-vironmental and system conditions with associatedutility values and time deadlines. Given these goalconditions, SA-POP uses current/expected conditions

Figure 1: Planning/Scheduling Representations in MACRO

to generate a scheduled plan of high expected util-ity (Kinnebrew et al., 2007).

3 MACRO COORDINATION

As described in Section 2.1, mission agents must ef-ficiently generate and coordinate plans and schedulesprovided by the TÆMS task decomposition trees andcriteria-directed scheduling. As shown in Figure 1,the leaves of a TÆMS task tree are methods, whichin standard TÆMS usage can be directly executed bythe agent. In MACRO, however, mission agents mustcommunicate these methods to their exec agents forresource-level planning/scheduling and actual execu-tion.

At the resource level, the decision-theoretic,first-principles planning and constraint-propagationscheduling is efficiently performed by SA-POP forachievement of goals in the dynamic sensor networkenvironment shown in Figure 1. Effectively employ-ing both representations and forms of planning andscheduling presents multiple challenges for coordina-tion between MACRO mission and exec agents.

3.1 Translation: Top-Down

Problem. For an exec agent to implement a TÆMSmethod, the mission agent must translate it into thegoal format used by SA-POP. SA-POP goals include

one or more goal conditions with associated utilityvalues and time deadlines. To plan for a goal accu-rately, SA-POP requires knowledge of expected sys-tem and environmental conditions at the time the planwill be executed. Although current conditions andother exec agent plans provide most of this informa-tion, other expected conditions may be the result ofmethods assigned to other exec agents in the missionagent’s current plan (i.e., other methods that enablethe method in question by satisfying some of its pre-conditions).Solution → Cross-references in task/goal mod-eling. Domain experts (e.g., scientists and engi-neers who design and deploy the sensor network)use MACRO’s domain-specific modeling language(based on GME (Karsai et al., 2003)) to specifythe TÆMS task tree for a mission agent. In thismodel, TÆMS methods are associated with neces-sary resource-level preconditions and goal conditions,which in turn are represented in the action networkmodel employed by the exec agent and SA-POP.Moreover, the domain expert can automatically derivemethod distributions for duration and outcome in thismodel by providing potential initial condition settings(with an associated probability) to SA-POP, whichproduces scheduled plans and summarizes their prob-ability of success, expected duration, and resource us-age.

Instead of directly executing a method, the mis-sion agent uses the encoded translation informa-

Figure 2: Planning/Scheduling Translation in MACRO

tion from the model to provide a goal to the execagent. This top-down translation is shown by the mis-sion agent to exec agent information transfer in Fig-ure 2. The mission agent awards overall task utility tomethods based on the quality aggregation functions(QAFs) and expected quality in the TÆMS task tree.

In the chosen decomposition of the TÆMS tasktree, parents with a QAF that requires execution ofall child subtasks/methods pass the full parent utilityto each child, while QAFs that allow any subset ofchildren pass a percentage of parent utility based onthe child’s percentage of total expected quality for theparent. For example, a task with an overall utility of100 that is decomposed into two subtasks of expectedquality 3 and 7 with a sum QAF would assign util-ity of 30 and 70, respectively, to its subtasks. Futurework will investigate more advanced methods of re-ward assignment in the decomposition of TÆMS tasktrees.

3.2 Translation: Bottom-Up

Problem. Another important challenge is codifyingthe bottom-up translation between SA-POP plans andTÆMS method parameters. Standard TÆMS meth-ods include a priori probability distributions for dura-tion and outcome quality, which are used during ini-tial criteria-directed scheduling by the mission agent.After an exec agent plans to achieve a goal, the re-sultant scheduled plan may imply significantly dif-

ferent probability distributions for the correspondingmethod. Similarly, as a plan is being executed bythe exec agent, there may be further changes to theexpected duration or probability of outcomes for theplan and its corresponding method. To improve theefficiency of future criteria-directed scheduling and totrigger appropriate mission-level re-scheduling, infor-mation about the exec agent’s plan must be commu-nicated to the mission agent.Solution → Summarize resource-level plans. In-stead of providing the complete resource-level planto the mission agent (whose format is ill-suited toits planning and scheduling capabilities), a MACROexec agent summarizes its plan by providing relevantinformation only, including (1) expected duration, (2)probability of achieving the goal, and (3) averageand maximum resource usage over expected execu-tion. The mission agent uses these values to updatemethod parameters with more accurate information,based on the resource-level planning and schedulingfor the current and expected environmental/systemconditions. The updated method parameters allow themission agent to more effectively perform any furtherplanning and scheduling for its task(s).

3.3 Context-Sensitive Updates

Problem. In addition to translating between the mis-sion and exec agent planning/scheduling representa-tions, MACRO agents must also decide when to up-

date and communicate the translated information. Inparticular, during execution of exec agent plans, de-viations may occur (e.g., differences between actualand expected duration of actions). Only some vari-ations, however, will impact the rest of the mission-level plan—or other plans—in a manner that wouldbe of interest to the mission agent.Solution → Leverage mission-level task context.Given the hierarchical relationship between missionand exec agents, the top-down decision to commu-nicate (i.e., when the mission agent should com-municate information to an exec agent) is relativelystraightforward. Specifically, whenever a new task isdecomposed/scheduled or method parameters in theplan are changed by re-planning/re-scheduling, themission agent communicates the new or revised goals(translated from the methods) to the assigned execagents.

For bottom-up updates, however, an exec agentcan use its knowledge of a mission agent’s overallgoals/interests to guide its decision of when to com-municate. Without mission agent guidance, an execagent would be forced to communicate on a peri-odic basis or whenever the execution deviates fromthe scheduled plan, which may happen frequently ina dynamic sensor network environment. When task-ing an exec agent with a goal, therefore, the MACROmission agents also provide guidance and contextualinformation, such as the optimization criteria for therelated task. Knowledge of the optimization criteriaallows the exec agent to configure SA-POP’s planningand scheduling to prefer plans based on that criteria.

In addition to optimization criteria, the missionagent can specify acceptable deviations (in either di-rection), success probability, expected utility, dura-tion, and resource usage of an executing plan. Thisinformation provides the exec agent with guidanceon the context for the corresponding method in themission agent’s plan, which allows the agent to moreintelligently determine when to update its scheduledplan and provide the revised summary to the missionagent. Specifically, during execution of a plan, theexec agent will only re-plan and re-schedule if the ex-pected utility falls below, or if the duration surpasses,specified thresholds. When other thresholds are ex-ceeded, the exec agent simply communicates updatedsummary information to the mission agent.

Figure 3 shows the execution of the resource-levelplan from Section 3.2. To demonstrate the benefit ofthe guidance/context provided by the mission agent,we focus on deviations of action duration from ex-pected duration in the critical path (i.e., the linkedsequence of actions that requires the longest time tocomplete). Although the planning and scheduling in

Figure 3: A Resource-level Plan (Critical Path Highlighted)

MACRO does not rely on identification of the criticalpath, such a path(s) always exist, and it constrains theexpected completion time of the plan.

Without the context provided by duration thresh-olds, the exec agent would have no knowledge of whatdeviations were important to the mission agent andwould have to communicate updates based on eachdeviation. It would recalculate its schedule every timean action did not complete with exactly its expectedduration. It would also transmit the new expected du-ration of the plan either with every recalculation or atleast every time an action finished outside of its sched-uled end window (either before or after that window).

The example execution in Figure 3 shows a typi-cal case in which the mission agent provides an over-threshold on duration equal to the difference betweenthe expected end-time of the plan and the originaldeadline. In other words, the mission agent is only in-terested in changes to the resource-level schedule thatwould result in its finishing later than the deadline. Inthis example, the exec agent would have to re-plan/re-schedule only when execution of action A6 goes be-yond its scheduled end window. Without the appro-priate context (i.e., the duration threshold), the execagent would have also had to unnecessarily recalcu-late or re-plan/re-schedule three times (after comple-tion of A1, A4, and A3) and communicate unneces-sary updates twice (after A1 and A4).

4 COORDINATION RESULTS

This section presents the results of mission and execagent coordination through the simulated execution ofrandomly-generated resource-level plans with a vari-ety of duration distributions for actions. These re-sults validate our claims that MACRO’s use of guided,context-sensitive coordination in planning/schedulingcan reduce communication and computation, while

still providing relevant information in a timely fash-ion.

4.1 Experimental Design

Our experiments simulate a scheduled, partial-orderplan generated by SA-POP for an exec agent at theresource level of MACRO. These plans include a setof actions with expected start and end time windows,as well as ordering links. For these experiments, weonly simulate cases in which a valid plan can be gen-erated.

One experimental parameter is the variability ofactual durations for actions, which requires differ-ent probability distributions parameterized by a sigmavalue. The experiments included both uniform dis-tributions and Gaussian (Normal) distributions. Theuniform distributions showed the same trends ob-served in the Gaussian distributions (results are omit-ted due to the length constraints). The action durationdistributions have a mean of 100 seconds and “low”and “high” variance scenarios providing a 95% like-lihood (for the Gaussian) that durations are within 25seconds or 75 seconds of the mean, respectively.

Another experimental variable is the length of thecritical path. The distributions provide all actionswith an expected duration of 100 seconds. The ex-pected time for completion of the plan therefore de-pends solely on the number of actions in the criticalpath.

The final experimental variable is the time thresh-old provided by the mission agent in MACROcontext-sensitive coordination, which determines howfar actions can surpass their expected end times be-fore the mission agent must be notified for potentialmission-level re-planning and re-scheduling. To as-sess computation and communication overhead of thecoordination mechanism, we employed random gen-eration of plans across a range of parameters ratherthan using a few example problems. These experi-ments do not assess the quality or utility of plans orpotential plan changes during coordination. MACROcoordination will not result in any degradation of planquality in comparison to the baseline coordination,however, since plan and schedule information thattriggers mission-level re-planning and re-schedulingis provided by both MACRO coordination mechanismand the baseline mechanism at the same time.

Since these experiments employ randomly-generated plans to cover a range of potential applica-tions, they do not allow changes to resource-level ormission-level plans during execution. Whenever anaction execution exceeded its scheduled end window,the schedule was updated and communicated to the

mission agent, but no changes to the plan or thresholdwere made. Without re-planning, the MACROcoordination overhead is an over-estimate of the realoverhead. After a critical path action’s end window isexceeded, execution of further actions will continueto exceed action end windows. Re-planning reducesthis possibility.

4.2 Experimental Results

Each experimental run included 10,000 trials with thegiven parameter settings. In each trial, a series of (n)actions formed the critical path, and each action hadan expected duration of 100 seconds. Using the cho-sen distribution, random values are generated that cor-respond to actual execution times. The number of up-dates and messages are calculated using those values.

4.2.1 Investigating Critical Path Length

These experiments were performed under the assump-tion that the mission agent simply requires a methodto be completed by the provided deadline and shouldonly be notified if the expected execution time willexceed that deadline. The threshold value is thereforeset to the difference between the deadline and the ex-pected duration of the plan. This threshold is variedin the experiments between 0 and 200 seconds in 5second increments.

Figure 4: The effect of critical path length with selectedthresholds with a low variance Gaussian

Figure 4 shows the information from the missionagent results in significantly less computation andcommunication than the baseline condition for all butthe smallest of critical paths The linear trend suggeststhat in the worst case (i.e., a tight threshold/deadline),MACRO sends about half as many messages as thebaseline machanism. As the threshold increases,MACRO performs even better, whereas the baselineperformance does not change.

Figure 5: The effect of critical path length with selectedthresholds with a high variance Gaussian

A comparison of the low variance action durationdistribution in Figure 4 to a high variance one in Fig-ure 5 shows that with the smallest thresholds a ratioof approximately 1 update per 2 actions in the criticalpath is required for both distributions. The 1:2 ra-tio is thus an approximate upper limit on the averagenumber of updates required in MACRO, even whenre-planning and re-scheduling is not possible.

The baseline mechanism shows a slight, relativeimprovement in the high variance case, but MACRO’scontext-sensitive coordination still requires far fewerupdates. However, the number of updates requiredin MACRO with different thresholds are much closerin the high variance case than the low variance case.This result suggests that when action durations areless certain, the critical path length is significantlymore important than the threshold, because even largethresholds can be exceeded by a series of actions thatbegins with an unexpectedly long-running action.

4.2.2 Investigating Time Thresholds

Figure 6 and Figure 7 show the trends in communi-cation and computation with respect to the durationthreshold. The baseline results are not included inthese figures because they do not use of the thresh-old value, therefore, they would produce a horizontalline close to the number of actions in the critical path.

These results show that as the threshold increases,the number of MACRO updates decreases. Figure 6,shows a steep initial decrease which levels off. Qual-itatively, this trend occurs since longer thresholds al-low a series of actions to exceed their expected dura-tion by a greater amount before requiring an update.Extreme variation, however, from expected durationscan occur and will still require some updates, evenwith relatively large thresholds. These results alsoshow, that even when uncertainty of action duration

Figure 6: The effect of Slack with selected critical paths ona low variance Gaussian

Figure 7: The effect of Slack with selected critical paths ona high variance Gaussian

is high, the exec agent can leverage the contextual in-formation provided by the mission agent to minimizecoordination overhead.

5 RELATED WORK

MACRO’s approach to planning and schedulingbuilds upon and extends a significant body ofrelated work. At the mission level, MACROagents employ Design-To-Criteria (DTC) plan-ning/scheduling (Wagner and Lesser, 2001) operatingon an augmented TÆMS task tree to efficiently op-timize for relevant criteria in generating a scheduledplan to perform assigned subtasks. At the resourcelevel, exec agents employ SA-POP (Kinnebrew et al.,2007) for decision-theoretic planning with constraint-propagation scheduling.

MACRO Agents communicate the most useful in-formation at an appropriate abstraction level and atthe right time. The translation from resource-levelplans to mission-level method parameters has somesimilarities to research that uses plan summary in-

formation to coordinate between agents employingHTN planning (e.g., (Clement and Durfee, 1999;Clement and Durfee, 2000)). MACRO mission andexec agents, however, employ different representa-tions for planning and scheduling. Moreover, the re-source and scheduling constraints in MACRO requiresummary information beyond the pre-, in-, and post-conditions used in Clement’s task summary info ap-proach (Clement and Durfee, 1999).

6 CONCLUDING REMARKS

This paper presented key research challenges forcoordinating planning and scheduling at two lev-els of a hierarchical multi-agent system. We dis-cussed MACRO’s solutions to coordinating HTNtask decomposition with criteria-directed schedulingand first-principles decision-theoretic planning withconstraint-propagation scheduling. We also reportthe results of experiments that showcased the bene-fits gained by employing MACRO’s guided, context-sensitive coordination of planning and scheduling.

Our experimental results quantified the effects ofdifferent distributions from which average durationinformation is derived for resource-level actions. Theexperiments also showcase the effects of other plan-ning/scheduling parameters, including the length of ascheduled plan’s critical path and the restrictivenessof the deadline. Moreover, our results verify the scal-ability of MACRO planning/scheduling coordinationwhen execution time is the primary criteria of inter-est to the mission agent. Our future work will exploreother forms of utility assignment in TÆMS task treedecomposition and evaluate the benefits of context-sensitive coordination with thresholds on plan char-acteristics other than execution time.

7 ACKNOWLEDGEMENTS

This work was supported in part by NASA AdvancedInformation Systems Technology (AIST) programunder grants NNA04AA69C and NNX06AG97G.

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