TY - JOUR
T1 - JUSTIFYING DIFFUSION APPROXIMATIONS FOR MULTICLASS QUEUEING NETWORKS UNDER A MOMENT CONDITION
AU - YE, Heng-Qing
AU - YAO, David D.
PY - 2018/12
Y1 - 2018/12
N2 - Multiclass queueing networks (MQN) are, in general, difficult objects to study analytically. The diffusion approximation refers to using the stationary distribution of the diffusion limit as an approximation of the diffusion-scaled process (say, the workload) in the original MQN. To validate such an approximation amounts to justifying the interchange of two limits, t → ∞ and k → ∞, with t being the time index and k, the scaling parameter. Here, we show this interchange of limits is justified under a p∗th moment condition on the primitive data, the interarrival and service times; and we provide an explicit characterization of the required order (p∗), which depends naturally on the desired order of moment of the workload process.
AB - Multiclass queueing networks (MQN) are, in general, difficult objects to study analytically. The diffusion approximation refers to using the stationary distribution of the diffusion limit as an approximation of the diffusion-scaled process (say, the workload) in the original MQN. To validate such an approximation amounts to justifying the interchange of two limits, t → ∞ and k → ∞, with t being the time index and k, the scaling parameter. Here, we show this interchange of limits is justified under a p∗th moment condition on the primitive data, the interarrival and service times; and we provide an explicit characterization of the required order (p∗), which depends naturally on the desired order of moment of the workload process.
KW - Diffusion limit
KW - Interchange of limits
KW - Multiclass queueing network
KW - Uniform stability
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U2 - 10.1214/18-AAP1401
DO - 10.1214/18-AAP1401
M3 - 21_Publication in refereed journal
VL - 28
SP - 3652
EP - 3697
JO - Annals of Applied Probability
JF - Annals of Applied Probability
SN - 1050-5164
IS - 6
ER -