TY - JOUR
T1 - Heavy-traffic limits for Discriminatory Processor Sharing models with joint batch arrivals
AU - Vis, P.
AU - Bekker, R.
AU - van der Mei, R. D.
AU - Núñez-Queija, R.
PY - 2020/3/1
Y1 - 2020/3/1
N2 - We study the performance of Discriminatory Processor Sharing (DPS) systems, with exponential service times and in which batches of customers of different types may arrive simultaneously according to a Poisson process. We show that the stationary joint queue-length distribution exhibits state-space collapse in heavy traffic: as the load ρ tends to 1, the scaled joint queue-length vector (1−ρ)Q converges in distribution to the product of a deterministic vector and an exponentially distributed random variable, with known parameters. The result provides new insights into the behavior of DPS systems. It shows how the queue-length distribution depends on the system parameters, and in particular, on the simultaneity of the arrivals. The result also suggests simple and fast approximations for the tail probabilities and the moments of the queue lengths in stable DPS systems, capturing the impact of the correlation structure in the arrival processes. Numerical experiments indicate that the approximations are accurate for medium and heavily loaded systems.
AB - We study the performance of Discriminatory Processor Sharing (DPS) systems, with exponential service times and in which batches of customers of different types may arrive simultaneously according to a Poisson process. We show that the stationary joint queue-length distribution exhibits state-space collapse in heavy traffic: as the load ρ tends to 1, the scaled joint queue-length vector (1−ρ)Q converges in distribution to the product of a deterministic vector and an exponentially distributed random variable, with known parameters. The result provides new insights into the behavior of DPS systems. It shows how the queue-length distribution depends on the system parameters, and in particular, on the simultaneity of the arrivals. The result also suggests simple and fast approximations for the tail probabilities and the moments of the queue lengths in stable DPS systems, capturing the impact of the correlation structure in the arrival processes. Numerical experiments indicate that the approximations are accurate for medium and heavily loaded systems.
KW - Batch arrivals
KW - Discriminatory Processor Sharing
KW - Heavy traffic
KW - Joint queue-length distribution
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U2 - 10.1016/j.orl.2020.01.004
DO - 10.1016/j.orl.2020.01.004
M3 - Article
AN - SCOPUS:85078848669
SN - 0167-6377
VL - 48
SP - 136
EP - 141
JO - Operations Research Letters
JF - Operations Research Letters
IS - 2
ER -