Details

Autor(en) / Beteiligte

• Guo, Yongjiang
• Hou, Xiyang
• Liu, Yunan

Titel

A functional law of the iterated logarithm for multi-class queues with batch arrivals

Ist Teil von

• Annals of operations research, 2021-05, Vol.300 (1), p.51-77

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2021

Quelle

EBSCOhost Business Source Ultimate

Beschreibungen/Notizen

• A functional law of the iterated logarithm (LIL) and its corresponding LIL are established for a multiclass single-server queue with first come first served (FCFS) service discipline. The functional LIL and its LIL quantify the magnitude of asymptotic stochastic fluctuations of the stochastic processes compensated by their deterministic fluid limits. The functional LIL and LIL are established in three cases: underloaded, critically loaded and overloaded, for performance measures including the total workload, idle time, queue length, workload, busy time, departure and sojourn time processes. The proofs of the functional LIL and LIL are based on a strong approximation approach, which approximates discrete performance processes with reflected Brownian motions. Numerical examples are considered to provide insights on these limit results.