Laws of Little in an open queueing network

The object of this research in the queueing theory is theorems about the functional strong laws of large numbers (FSLLN) under the conditions of heavy traffic in an open queueing network (OQN). The FSLLN is known as a fluid limit or fluid approximation. In this paper, FSLLN are proved for the values of important probabilistic characteristics of the OQN investigated as well as the virtual waiting time of a customer and the queue length of customers. As applications of the proved theorems laws of Little in OQN are presented

New results on rewrite-based satisfiability procedures

Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T. If a sound and complete inference system for first-order logic is guaranteed to terminate on T-satisfiability problems, any theorem-proving strategy with that system and a fair search plan is a T-satisfiability procedure. We prove termination of a rewrite-based first-order engine on the theories of records, integer offsets, integer offsets modulo and lists. We give a modularity theorem stating sufficient conditions for termination on a combinations of theories, given termination on each. The above theories, as well as others, satisfy these conditions. We introduce several sets of benchmarks on these theories and their combinations, including both parametric synthetic benchmarks to test scalability, and real-world problems to test performances on huge sets of literals. We compare the rewrite-based theorem prover E with the validity checkers CVC and CVC Lite. Contrary to the folklore that a general-purpose prover cannot compete with reasoners with built-in theories, the experiments are overall favorable to the theorem prover, showing that not only the rewriting approach is elegant and conceptually simple, but has important practical implications.Comment: To appear in the ACM Transactions on Computational Logic, 49 page

Using network calculus to optimize the AFDX network

This paper presents quantitative results we obtained when optimizing the setting of priorities of the AFDX traffic flows, with the objective to obtain tighter latency and queue-size deterministic bounds (those bounds are calculated by our Network Calculus tool). We first point out the fact that setting randomly the priorities gives worse bounds than using no priorities, and we then show experiments on the basis of classic optimization techniques such as a descent method and a tentative AlphaBetaassisted brute-force approach: both of them haven’t brought significantly better results. We finally present experiments based on genetic algorithms, and we show how driving these algorithms in an adequate way has allowed us to deliver a full range of priority configurations that bring tighter bounds and allow the network traffic designer to trade off average gains of 40% on all the latency bounds against focused improvement on the largest queue-size bound (up to a 30% reduction)

Prominence in queuing: queue length versus basket size

Choosing checkouts in a supermarket is a common consumer decision that has been largely overlooked in previous research. In this paper, we investigate the relative impact of queue length and average basket size on consumers’ waiting time expectations and checkout choice. Four studies highlight the importance of basket content, leading to a preference for longer queues where consumers have little loaded shopping baskets than shorter queues with fully loaded baskets. However, queuing perceptions change when focusing consumers’ attention on the time cost of payment at the checkout

T-Cell activation: a queuing theory analysis at low agonist density

We analyze a simple linear triggering model of the T-cell receptor (TCR) within the framework of queuing theory, in which TCRs enter the queue upon full activation and exit by downregulation. We fit our model to four experimentally characterized threshold activation criteria and analyze their specificity and sensitivity: the initial calcium spike, cytotoxicity, immunological synapse formation, and cytokine secretion. Specificity characteristics improve as the time window for detection increases, saturating for time periods on the timescale of downregulation; thus, the calcium spike (30 s) has low specificity but a sensitivity to single-peptide MHC ligands, while the cytokine threshold (1 h) can distinguish ligands with a 30% variation in the complex lifetime. However, a robustness analysis shows that these properties are degraded when the queue parameters are subject to variation—for example, under stochasticity in the ligand number in the cell-cell interface and population variation in the cellular threshold. A time integration of the queue over a period of hours is shown to be able to control parameter noise efficiently for realistic parameter values when integrated over sufficiently long time periods (hours), the discrimination characteristics being determined by the TCR signal cascade kinetics (a kinetic proofreading scheme). Therefore, through a combination of thresholds and signal integration, a T cell can be responsive to low ligand density and specific to agonist quality. We suggest that multiple threshold mechanisms are employed to establish the conditions for efficient signal integration, i.e., coordinate the formation of a stable contact interface