[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85570-en":3,"doc-seo-85570-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":11,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},85570,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1782875107921204101",8,"Research & Report","Robust Fleet Sizing for Multi-UAV Inspection Missions under Synchronized Replacement Demand","Multi-UAV inspection missions rely on spare drones to replace active units during battery recharge cycles, but common fleet-sizing models assume steady-state operation or treat replacement requests as independent. For finite-horizon missions, this independence can fail at mission level when demands cluster. The work pinpoints a structural failure mode caused by energy-aware routing that synchronizes battery depletion, producing replacement bursts that exhaust the spare pool. A closed-form sufficient rule k = m(⌈R⌉ + 1) is derived using the recovery-to-active time ratio R, with Monte Carlo tests achieving 99.8% mission success.","Robust Fleet Sizing for Multi-UAV Inspection Missions under Synchronized Replacement Demand  \nVishal Ramesh and Antony Thomas  \nRobotics Research Center, IIIT Hyderabad, Hyderabad 500032, India  \narXiv :2604 . 15890v2 [ cs .RO] 11 Jul 2026  \nAbstract—Multi-UAV inspection missions require spare drones to replace active drones during recharging cycles. Existing fleetsizing approaches often assume steady-state operating conditions that do not apply to finite-horizon missions, or they treat replacement requests as statistically independent events. The latter provides per-request blocking guarantees that fail to translate to mission-level reliability when demands cluster. This paper identifies a structural failure mode where efficient routing assigns similar workloads to each UAV, leading to synchronized battery depletion and replacement bursts that exhaust the spare pool even when average capacity is sufficient. We derive a closedform sufficient fleet-sizing rule, k = m (⌈R⌉ + 1), where mis the number of active UAVs and R is the recovery-to-active time ratio. This additive buffer of m spares absorbs worst-case synchronized demand at recovery-cycle boundaries and ensures mission-level reliability even when all UAVs deplete simultaneously. Monte Carlo validation across five scenarios (m ∈ [2 , 10], R ∈ [0 .87 , 3.39], 1000 trials each) shows that Erlang-B sizing with a per-request blocking target ε = 0 .01 drops to 69.9% mission success at R = 3 .39, with 95% of spare exhaustion events concentrated in the top-decile 5-minute demand windows. In contrast, the proposed rule maintains 99.8% success (Wilson 95% lower bound 99.3%) across all tests, including wind variability up to CV = 0 .30, while requiring only four additional drones in the most demanding scenario.  \nIndex Terms—Multi-Robot Systems, Aerial Systems: Applications, Task and Resource Allocation, Robust Planning  \nI. INTRODUCTION  \nBATTERY-LIMITED endurance poses a fundamental bot  \ntleneck in multi-UAV inspection missions. In applications such as infrastructure inspection, precision agriculture, and environmental monitoring, a team of UAVs must service a finite set of distributed sites whose aggregate workload exceeds the endurance of any single vehicle [5], [6] . Sustained operation therefore necessitates periodic withdrawal of active UAVs for battery replenishment, with immediate replacement by spare units drawn from a shared fleet. If a replacement vehicle is unavailable at the time of request, mission continuity is compromised. Consequently, determining the minimum number of spare UAVs required to guarantee uninterrupted task execution constitutes a critical planning and resource allocation problem. Existing fleet-sizing approaches typically rely on one of two modeling assumptions. The first is steady-state operation, where vehicles cycle indefinitely and spare capacity follows from average utilization [1]–[3] . The second treats replacement requests as statistically independent, sizing the spare pool so each request is served with probability at least 1 − ε [4] . Both assumptions are ill-suited to finite-horizon inspection missions. Steady-state models do not account for transient de-  \nFig. 1. Operational cycle of a multi-UAV inspection mission. Energy-aware routing assigns similar workloads, producing synchronized battery depletion. The fleet-sizing rule determines the spare count k from mission parameters m and R = ¯Trecovery/¯Tactive.  \nmand in missions where each task is completed exactly once. Independence-based models guarantee per-request blocking but not mission-level reliability. Even ε = 0.01 yields mission success well below 95% over dozens of handovers.  \nA key observation of this work is that finite inspection missions induce synchronized, rather than independent, replacement demand. Energy-aware routing assigns UAVs to spatially clustered sites, leading to similar travel distances and comparable battery depletion rates across vehicles. Consequently, repl","cbCaif6m8N10XNsM","https://ap.wps.com/l/cbCaif6m8N10XNsM","pdf",652308,3,1,"English","en",105,"# Introduction\n## Mission Setting and Problem Statement\n## Limitations of Existing Fleet-Sizing Models\n## Synchronized Replacement Demand and Failure Mode\n# Related Work\n## Modeling Dimensions for UAV Replacement","[{\"question\":\"Why do steady-state or independent replacement models underperform for finite-horizon inspection missions?\",\"answer\":\"Steady-state models ignore transient demand across a finite set of one-time tasks, and independent models guarantee per-request blocking without ensuring mission-level reliability when replacement demands cluster.\"},{\"question\":\"What structural failure mode does the paper identify for multi-UAV inspection missions?\",\"answer\":\"Energy-aware routing can assign similar workloads to UAVs, causing synchronized battery depletion and replacement bursts that can exhaust the spare pool even when average capacity seems sufficient.\"},{\"question\":\"How is the proposed fleet-sizing rule computed and what does it guarantee?\",\"answer\":\"The rule uses k = m(⌈R⌉ + 1), where m is the number of active UAVs and R is the recovery-to-active time ratio; it provides a closed-form additive buffer of m spares to absorb worst-case synchronized demand at recovery-cycle boundaries, maintaining high mission success.\"}]",1784204667,20,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"robust-fleet-sizing-for-multi-uav-inspection-missions-under-synchronized-replacement-demand","",{"@graph":35,"@context":84},[36,52,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,49],{"item":40,"name":41,"@type":42,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":20},"https://docshare.wps.com/document/research-report/",{"item":50,"name":13,"@type":42,"position":51},"https://docshare.wps.com/document/robust-fleet-sizing-for-multi-uav-inspection-missions-under-synchronized-replacement-demand/85570/",4,{"url":50,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":23,"description":14,"dateModified":60,"datePublished":61,"encodingFormat":59,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":40,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":20},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"Why do steady-state or independent replacement models underperform for finite-horizon inspection missions?","Question",{"text":74,"@type":75},"Steady-state models ignore transient demand across a finite set of one-time tasks, and independent models guarantee per-request blocking without ensuring mission-level reliability when replacement demands cluster.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What structural failure mode does the paper identify for multi-UAV inspection missions?",{"text":79,"@type":75},"Energy-aware routing can assign similar workloads to UAVs, causing synchronized battery depletion and replacement bursts that can exhaust the spare pool even when average capacity seems sufficient.",{"name":81,"@type":72,"acceptedAnswer":82},"How is the proposed fleet-sizing rule computed and what does it guarantee?",{"text":83,"@type":75},"The rule uses k = m(⌈R⌉ + 1), where m is the number of active UAVs and R is the recovery-to-active time ratio; 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