Analysis of a tripartite entanglement distribution switch

Queueing Systems - We study a quantum switch that distributes tripartite entangled states to sets of users. The entanglement switching process requires two steps: First, each user attempts to...     

On optimal polling policies

In a single-server polling system, the server visits the queues according to a routing policy and while at a queue, serves some or all of the customers there according to a service policy. A polling (or scheduling) policy is a sequence of decisions on whether to serve a customer, idle the server, or switch the server to another queue. The goal of this paper is to find polling policies that stochastically minimize the unfinished work and the number of customers in the system at all times. This optimization problem is decomposed into three subproblems: determine the optimal action (i.e., serve, switch, idle) when the server is at a nonempty queue; determine the optimal action (i.e., switch, idle) when the server empties a queue; determine the optimal routing (i.e., choice of the queue) when the server decides to switch. Under fairly general assumptions, we show for the first subproblem that optimal policies are greedy and exhaustive, i.e., the server should neither idle nor switch when it is at a nonempty queue. For the second subproblem, we prove that in symmetric polling systems patient policies are optimal, i.e., the server should stay idling at the last visited queue whenever the system is empty. When the system is slotted, we further prove that non-idling and impatient policies are optimal. For the third subproblem, we establish that in symmetric polling systems optimal policies belong to the class of Stochastically Largest Queue (SLQ) policies. An SLQ policy is one that never routes the server to a queue known to have a queue length that is stochastically smaller than that of another queue. This result implies, in particular, that the policy that routes the server to the queue with the largest queue length is optimal when all queue lengths are known and that the cyclic routing policy is optimal in the case that the only information available is the previous decisions.This work was supported in part by NSF under Contract ASC-8802764.     

Application of the extended Barshay-Temmer theorem to heavy-ion reactions

The reactions ¹⁰B+¹²C, ¹⁴N+¹⁶O leading to various final states in the isobaric mass systems 11, 13 and 15, respectively, have been investigated experimentally. These measurements provide a number of applications for the extended Barshay-Temmer theorem.     

Bounds for a class of stochastic recursive equations

In this note we develop a framework for computing upper and lower bounds of an exponential form for a class of stochastic recursive equations with uniformly recurrent Markov modulated inputs. These bounds generalize Kingman's bounds for queues with renewal inputs.     

Quadrupole moments and the structure of the even titanium and chromium nuclei

The energies of the six circular transitions (n = 13 → n = 12 through n = 8 → n = 7) of the K^?Pb exotic atom have been measured to high precision (typically ～ 50 ppm) using Ge (Li) spectrometers. The data acquisition system was computer controlled and stabilized, the energy calibration spectrum was taken simultaneously with the data spectrum. The experimental energies of the six transitions were corrected for ADC nonlinearities and data-calibration spectrum shifts, as well as the presence of unresolved noncircular transition contaminants. The energies of five of the transitions (13 → 12 through 9 → 8) were computed from quantum electrodynamics, including all significant orders of vacuum polarization, electron screening and nuclear polarization. The mass of the K^? was adjusted to achieve a best fit with the experimental energies: the result was m_K^? = 493.657 ± 0.020 MeV.     

Burst reduction properties of rate-control throttles: departure process

In this paper we study the departure processes of two rate-control throttles: the token bank and the leaky bucket. Using sample path methods and the notion of majorization, we analyze the effect that parameters such as the token buffer capacity and token generation rate have on the vector of interdeparture times. In the transient case, we establish the monotonicity of the burst reduction in the sense of the majorization. In the case that the departure process converges in coupling to a stationary and ergodic process, the transient comparison results allow us to establish the monotonicity of the stationary interdeparture times in the sense of the convex ordering. Comparisons between the two flow control schemes are also established when appropriate.The work of this author was supported in part by the CEC DG XIII under the ESPRIT BRA grant QMIPS.The work of this author was supported in part by the National Science Foundation under grants ASC 88-8802764 and NCR-9116183.     

The customer response times in the processor sharing queue are associated

The customer response times in the egalitarian processor sharing queue are shown to be associated random variables under renewal inputs and general independent service times assumptions.The work by this author was supported in part by the National Science Foundation under grant ASC 88-8802764 and by the Office of Naval Research under grant ONR N00014-87-K-0796.     

Sample path methods in the control of queues

Sample path methods are now among the most used techniques in the control of queueing systems. However, due to the lack of mathematical formalism, they may appear to be non-rigorous and even sometimes mysterious. The goal of this paper is threefold: to provide a general mathematical setting, to survey the most popular sample path methods including forward induction, backward induction and interchange arguments, and to illustrate our approach through the study of a number of classical scheduling and routing optimization problems arising in queueing theory.Z. Liu was supported in part by the CEC DG XIII under the ESPRIT BRA grants QMIPS.P. Nain was supported in part by NSF under grant NCR-9116183 and by the CEC DG XIII under the ESPRIT BRA grants QMIPS.D. Towsley was supported in part by NSF under grant NCR-9116183.     

Effects of service disciplines inG/GI/s queueing systems

Transient extremal properties of some service disciplines are established in theG/GI/s queueing system for the minimization and maximization of the expectations of the Schur convex functions, convex symmetric functions and the sums of convex functions of the waiting times, response times, lag times and latenesses. When resequencing is required in the system, the FCFS and LCFS disciplines are shown to minimize and maximize, respectively, the expectations of any increasing functions of the end-to-end delays. All of these results are presented in terms of stochastic orderings. The paper concludes with extensions of the results to the stationary regime and to tandem as well as general queueing networks.This work was supported in part by the National Science Foundation under grant ASC 88-8802764.The work of this author was also partially supported by CEC DG-XIII under the ESPRIT-BRA grant QMIPS.