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 gainscan be attained by employing multiple planning and scheduling mechanisms that are each tailored to theparticular agent roles. This paper presents such a framework for a global sensor web, operating as a two-level hierarchy: (1) the mission level for global coordination of complex tasks, and (2) the resource level foroperation of subtasks on individual sensor networks. We describe important challenges in coordinating amongagents employing two different planning and scheduling methods and develop a coordination solution for thisframework. Experimental results validate the benefits of employing guided, context-sensitive coordination ofplanning and scheduling in such 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 hierarchy:(1) the mission level where global coordination across

sensor networks is achieved, and (2) the resource levelwhere operation of the local sensor network is coordi-nated and controlled. Agents at these different levelsof the system operate in different contexts that implydifferent planning and scheduling requirements.

At the mission level, multiple sensor networksmust coordinate to allocate their limited resources torequested tasks in a manner that provides a high sys-tem utility. Moreover, they must coordinate plan-ning and scheduling at an appropriate level of ab-straction to avoid computational intractability. At theresource level, individual sensor networks must per-form detailed planning and scheduling to complete as-signed subtasks in dynamic, uncertain, and resource-constrained, environments.

These differences suggest that significant effi-ciency and capability gains may be achieved by em-ploying different planning and scheduling techniquestailored to the particular requirements at each level.Developing such an agent architecture, however, alsopresents challenges in coordinating among the agentsthat use different planning and scheduling mecha-nisms. In particular, employing different planning andscheduling mechanisms at the mission and resourcelevels requires an appropriate translation of the task,

plan, and schedule representations between levels. Italso requires a coordination mechanism for decidingwhen to exchange information between levels duringplan 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,which are responsible for the operation of the sensornetwork hardware. Each exec agent controls a set ofcomputational/sensor resources within the sensor net-work and is supported by additional domain-specificagents. An exec agent also employs services for plan-ning, scheduling, allocation, and resource manage-ment of the hardware under its control. These ser-vices are shared with any supporting agents under itsdirection, providing a centralized control and environ-mental awareness for its set of resources.

2.1 MACRO Mission Level

At the mission level of a sensor web MAS, user tasksand scheduled plans spanning multiple sensor net-works have a high degree of complexity. Hierarchi-cal analysis helps deal with this complexity, both for

problem/task representation by domain experts andfor coordinated planning and scheduling among mul-tiple agents. Therefore, MACRO employs a modi-fied implementation of the Task Analysis, Environ-ment Modeling, and Simulation (TÆMS) (Horlinget al., 1999) language, which provides a hierarchicaltask network representation for multi-agent planningand scheduling.

MACRO incorporates the OGC SensorML (Bottset al., 2007) representation of sensors and data pro-cessing with the TÆMS hierarchically decomposabletask representation. This provides standardized de-scriptions of task/subtask requirements and effectsacross sensor networks. The TÆMS representationalso allows the specification of discrete probabilitydistributions for task/subtask characteristics includingpotential 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 common to the resource level. More-over, SA-POP provides incremental re-planning/re-scheduling that can quickly revise scheduled plansduring execution and prevent more expensive re-planning/re-scheduling at the mission level. Inconjunction with SA-POP, exec agents also em-ploy the Resource Allocation and Control Engine(RACE) (Shankaran et al., 2007) for resource allo-

Figure 1: Planning/Scheduling Representations in MACRO

cation and management to meet scheduled deadlinesand required quality of service (QoS) parameters fordeployed applications and hardware-based actions.

First-principles planning and scheduling with SA-POP requires a set of goal conditions that correspondto the desired outcome. These goal conditions arespecified as desired environmental and system condi-tions with associated utility values and time deadlines.Given these goal conditions, SA-POP uses current/-expected conditions to generate a scheduled plan ofhigh expected utility (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 executedby the agent. In MACRO, however, mission agentsmust communicate these methods to their exec agentsfor resource-level planning/scheduling and actual ex-ecution. 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 includeone 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. In MACRO, domain experts (e.g., scientistsand engineers who design and deploy the sensor net-work) employ a domain-specific modeling language,defined using the Generic Modeling Environment(GME) (Karsai et al., 2003)), to specify the TÆMStask tree for a mission agent. In this model, TÆMSmethods are associated with necessary resource-levelpreconditions and goal conditions, which are, in turn,represented in the action network model employed by

Figure 2: Planning/Scheduling Translation in MACRO

the exec agent and SA-POP. Moreover, the domainexpert can automatically derive method distributionsfor duration and outcome in this model by providingpotential initial condition settings (with an associatedprobability) to SA-POP, which produces scheduledplans and summarizes their probability of success, ex-pected duration, and resource usage.

Instead of directly executing a method, the mis-sion agent uses the encoded translation informa-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 util-ity to each child, while QAFs that allow any subsetof children pass a percentage of parent utility basedon the child’s percentage of total expected quality forthe parent. For example, a task with an overall utilityof 100 that is decomposed into two subtasks of ex-pected quality 3 and 7 with a sum QAF would assignutility of 30 and 70, respectively, to its subtasks. Infuture work, we intend to investigate more advancedmethods of reward assignment in the decompositionof TÆMS task trees.

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.Instead 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 scheduling

for 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 con-text. Given the hierarchical relationship between mis-sion and exec agents, the top-down decision to com-municate (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 thresholds for deviation (in eitherdirection) of an executing plan on success probability,expected utility, duration, and resource usage. Thisinformation provides the exec agent with guidanceon the context for the corresponding method in themission agent’s plan. This context allows the agentto more intelligently determine when to update itsscheduled plan and provide the revised summary tothe mission agent. Specifically, during execution of aplan, the exec agent will only re-plan and re-scheduleif the expected utility falls below an under-threshold

or if the duration surpasses an over-threshold. When-ever any other threshold is exceeded, the exec agentwill simply communicate updated summary informa-tion to the mission agent.

Figure 3 shows the execution of the resource-levelplan from Section 3.2. To demonstrate the benefit of

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

the 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 inMACRO 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 an over-thresholdon duration, the exec agent would have no knowl-edge of what deviations were important to the missionagent and would have to communicate updates basedon each deviation. It would recalculate its scheduleevery time an action did not complete with exactlyits expected duration. Further, it would have to trans-mit the new expected duration of the plan either withevery recalculation, or at least every time an actionfinished outside of its scheduled end window (eitherbefore 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, in the form of the duration threshold,the exec agent would have also had to unnecessar-ily recalculate or re-plan/re-schedule three times (af-

ter completion of A1, A4, and A3) and communicateunnecessary 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 resultsvalidate our claims in Section 3 that MACRO’s use ofguided, context-sensitive coordination in planning/-scheduling can reduce communication and computa-tion, while still providing relevant information in atimely fashion.

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, al-though the results for the uniform distributions areomitted due to length constraints. The uniform dis-tributions, however, showed the same trends observedin the Gaussian distributions and required even lessMACRO computation and communication for boththe baseline and context-sensitive coordination mech-anisms. The action duration distributions have a meanof 100 seconds and “low” and “high” variance scenar-ios providing a 95% likelihood (for the Gaussian) thatdurations are within 25 seconds or 75 seconds of themean, 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, which deter-mines how far actions can surpass their expected endtimes before re-planning and re-scheduling are re-quired for MACRO context-sensitive coordination. Inthese experiments, we used a worst case scenarioin which neither the resource-level nor mission-level

plans could be changed during execution. When-ever an action execution went beyond its scheduledend window, therefore, the schedule was updated andcommunicated to the mission agent but no changesto the plan or threshold were made. Disallowing re-planning/re-scheduling allows the experiments to userandomly-generated plans across a range of parame-ters rather than a few example problems. It also re-sults in significantly more computation and commu-nication, however, since future actions are likely tocontinue going beyond their end windows after a crit-ical path action’s end window is exceeded.

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 complete by the provided deadline and should onlybe notified if the expected execution will exceed thatdeadline. The threshold value is therefore set to thedifference between the deadline and the expected du-ration of the plan. This threshold is varied in the ex-periments between 0 seconds and 200 seconds by 5second increments.

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

Figure 4 shows how MACRO’s use of thresholdinformation from the mission agent results in sig-nificantly less computation and communication thanthe baseline for everything but the smallest of criti-cal paths The linear nature of the data suggests that

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

in the worst case (i.e., a tight threshold/deadline),MACRO sends about half as many messages as thebaseline. As the threshold increases, MACRO per-forms even better, whereas the baseline performancedoes not change.

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 is not included in these fig-ures because it does not make use of the thresholdvalue. If included, it would be a constant line close tothe number of actions in the critical path.

The trend in these results shows that as the thresh-old increases, the number of MACRO updates de-creases close to exponentially. This exponential de-cay results from the fact that longer thresholds allow aseries of actions to exceed their expected duration bya greater amount before requiring an update, but that

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

extreme variation from expected durations can occurand will still require some updates, even with rela-tively large thresholds. These results also show, how-ever, that even when uncertainty of action duration ishigh, the exec agent can leverage the contextual in-formation provided by the mission agent to minimizecomputation and communication.

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) operat-ing on an augmented TÆMS task tree to efficientlyoptimize for relevant criteria in generating a sched-uled plan to perform assigned subtasks. While, atthe resource level, exec agents employ SA-POP (Kin-nebrew et al., 2007) for decision-theoretic planningwith constraint-propagation scheduling.

MACRO coordinates agents employing its two

planning/scheduling mechanisms to communicate themost useful information at an appropriate abstrac-tion level and at the right time. The translation fromresource-level plans to mission-level method parame-ters has some similarities to research that uses plansummary information to coordinate between agentsemploying HTN planning (e.g., (Clement and Durfee,1999; Clement and Durfee, 2000)). MACRO missionand exec agents, however, employ different represen-tations for planning and scheduling. Moreover, theresource and scheduling constraints in MACRO re-quire summary information beyond the pre-, in-, andpost-conditions used in Clement’s task summary infoapproach (Clement and Durfee, 1999).

The MACRO translation between mission agentmethods and exec agent goals provides similar plan-ning summary information at a level of abstrac-tion determined by the hierarchical divide betweentheir domain representations. In addition, MACROexec agents summarize scheduling, probability, andresource-usage information that can be used by mis-sion agents employing TÆMS task tree decomposi-tion with criteria-directed scheduling.

6 CONCLUDING REMARKS

This paper presents some key research challenges forcoordinating planning and scheduling at two levelsof a hierarchical multi-agent system. In particular,we discuss MACRO’s solutions to coordinating HTNtask decomposition with criteria-directed schedul-ing and first-principles decision-theoretic planningwith constraint-propagation scheduling. Finally, weconducted experiments that showcased the benefitsgained 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. In future work, we intend toexplore other forms of utility assignment in TÆMStask tree decomposition and evaluate the benefits ofcontext-sensitive coordination with thresholds on plancharacteristics other than execution time.

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