IEEE/ACM Transactions on Networking (TON)
IEEE/ACM Transactions on Networking (TON)
A multiclass station with Markovian feedback in heavy traffic
Mathematics of Operations Research
Mathematics of Operations Research
New linear program performance bounds for queueing networks
Journal of Optimization Theory and Applications - Special issue in honor of Yu-Chi Ho
Stability of networks and protocols in the adversarial queueing model for packet routing
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Mathematics of Operations Research
Journal of the ACM (JACM)
Universal-stability results and performance bounds for greedy contention-resolution protocols
Journal of the ACM (JACM)
Stability of Adaptive and Nonadaptive Packet Routing Policies in Adversarial Queueing Networks
SIAM Journal on Computing
Operations Research
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
Robust solutions of uncertain linear programs
Operations Research Letters
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Performance analysis of queueing networks is one of the most challenging areas of queueing theory. Barring very specialized models such as product-form type queueing networks, there exist very few results that provide provable nonasymptotic upper and lower bounds on key performance measures. In this paper we propose a new performance analysis method, which is based on the robust optimization. The basic premise of our approach is as follows: rather than assuming that the stochastic primitives of a queueing model satisfy certain probability laws---such as i.i.d. interarrival and service times distributions---we assume that the underlying primitives are deterministic and satisfy the implications of such probability laws. These implications take the form of simple linear constraints, namely, those motivated by the law of the iterated logarithm (LIL). Using this approach we are able to obtain performance bounds on some key performance measures. Furthermore, these performance bounds imply similar bounds in the underlying stochastic queueing models. We demonstrate our approach on two types of queueing networks: (a) tandem single-class queueing network and (b) multiclass single-server queueing network. In both cases, using the proposed robust optimization approach, we are able to obtain explicit upper bounds on some steady-state performance measures. For example, for the case of TSC system we obtain a bound of the form C(1-ρ)-1 ln ln((1-ρ)-1) on the expected steady-state sojourn time, where C is an explicit constant and ρ is the bottleneck traffic intensity. This qualitatively agrees with the correct heavy traffic scaling of this performance measure up to the ln ln((1-ρ)-1) correction factor.