Bursty Arrivals, Smooth Sojourns: Non-Poissonian Temporal Dynamics in a Logistics Warehouse

Abstract

Warehouses are central nodes in logistics networks: they buffer material flows, synchronize heterogeneous actors, and absorb temporal mismatches between inbound and outbound operations. Yet most warehouse analyses still rely on aggregate performance indicators or on queueing assumptions in which event timing is stationary and approximately memoryless. Here we use one month of high-resolution pallet-level data from a large Spanish warehouse to characterize arrivals, departures, and outbound residence times from a statistical-physics perspective. Inter-arrival and inter-departure times are strongly heterogeneous and compatible with heavy-tailed, non-Poissonian behavior, whereas outbound sojourn times are more naturally described by a log-normal distribution, suggesting constrained service mechanisms with a characteristic operational scale. Disaggregation by logistics flow reveals systematic differences in burstiness, memory, and distributional similarity. A renewal-based aging analysis uncovers recurrent weekly accumulation and clearance cycles in the outbound buffer zone. Finally, a Little's-Law-inspired activity--sojourn scaling identifies two operational regimes: a near-linear baseline under regular turnover and a reproducible off-baseline branch associated with weekend accumulation and Monday dispatches. These results provide a compact diagnostic framework for temporal complexity in warehouse operations and show how limited but high-resolution industrial data can reveal operational structure invisible to aggregate throughput statistics.