Rate conservation laws: A survey

We survey the rate conservation law, RCL for short, arising in queues and related stochastic models. RCL was recognized as one of the fundamental principles to get relationships between time and embedded averages such as the extended Little's formulaH=G, but we show that it has other applications. For example, RCL is one of the important techniques for deriving equilibrium equations for stochastic processes. It is shown that the various techniques, including Mecke's formula for a stationary random measure, can be formulated as RCL. For this purpose, we start with a new definition of the rate with respect to a random measure, and generalize RCL by using it. We further introduce the notion of quasi-expectation, which is a certain extension of the ordinary expectation, and derive RCL applicable to the sample average results. It means that the sample average formulas such asH=G can be obtained as the stationary RCL in the quasi-expectation framework. We also survey several extensions of RCL and discuss examples. Throughout the paper, we would like to emphasize how results can be easily obtained by using a simple principle, RCL.     

Light tail asymptotics in multidimensional reflecting processes for queueing networks

We are concerned with the stationary distributions of reflecting processes on multidimensional nonnegative orthants and other related processes, provided they exist. Such stationary distributions arise in performance evaluation for various queueing systems and their networks. However, it is very hard to obtain them analytically, so our interest is directed to analytically tractable characteristics. For this, we consider tail asymptotics of the stationary distributions.     

Decomposability in queues with background states

A symmetric queue is known to have a nice property, the so-called insensitivity. In this paper, we generalize this for a single node queue with Poisson arrivals and background state, which changes at completion instants of lifetimes as well as at the arrival and departure instants. We study this problem by using the decomposability property of the joint stationary distribution of the queue length and supplementary variables, which implies the insensitivity. We formulate a Markov process representing the state of the queue as an RGSMP (reallocatable generalized semi-Markov process), and give necessary and sufficient conditions for the decomposability. We then establish general criteria to be sufficient for the queue to possess the property. Various symmetric-like queues with background states, including continuous time versions of moving server queues, are shown to have the decomposability.This author is partially supported by NEC C&C Laboratories.     

Structure-reversibility and departure functions of queueing networks with batch movements and state dependent routing

We consider characterizations of departure functions in Markovian queueing networks with batch movements and state-dependent routing in discrete-time and in continuous-time. For this purpose, the notion of structure-reversibility is introduced, which means that the time-reversed dynamics of a queueing network corresponds with the same type of queueing network. The notion is useful to derive a traffic equation. We also introduce a multi-source model, which means that there are different types of outside sources, to capture a wider range of applications. Characterizations of the departure functions are obtained for any routing mechanism of customers satisfying a recurrent condition. These results give a unified view to queueing network models with linear traffic equations. Furthermore, they enable us to consider new examples as well as show limited usages of this kind of queueing networks. This revised version was published online in June 2006 with corrections to the Cover Date.     

Alternating copolymerization of polar vinyl monomers in the presence of zinc chloride. II. Properties of acrylonitrile–styrene copolymer

The properties of the acrylonitrile–styrene copolymer prepared in the presence of zinc chloride were investigated in comparison with those of a copolymer having the same overall composition and prepared by the ordinary radical procedure. The characteristics of the polymer prepared with ZnCl₂ were as follows: (1) less coloration by alkali treatment, (2) less coloration by thermal treatment and (3) higher glass transition temperature. These features may be attributed principally to the structure of the copolymer, which has more unlike bonds and less long sequences as described in the first article of this series. The effects of residual salt in the copolymer on the properties were also investigated.     

Structure and catalytic properties of carboxylesterase isozymes involved in metabolic activation of prodrugs

Mammalian carboxylesterases (CESs) comprise a multigene family whose gene products play important roles in biotransformation of ester- or amide-type prodrugs. They are members of an alpha,beta-hydrolase-fold family and are found in various mammals. It has been suggested that CESs can be classified into five major groups denominated CES1-CES5, according to the homology of the amino acid sequence, and the majority of CESs that have been identified belong to the CES1 or CES2 family. The substrate specificities of CES1 and CES2 are significantly different. The CES1 isozyme mainly hydrolyzes a substrate with as mall alcohol group and large acyl group, but its wide active pocket sometimes allows it to act on structurally distinct compounds of either a large or small alcohol moiety. In contrast, the CES2 isozyme recognizes a substrate with a large alcohol group and small acyl group, and its substrate specificity may be restricted by the capability of acyl-enzyme conjugate formation due to the presence of conformational interference in the active pocket. Since pharmacokinetic and pharmacological data for prodrugs obtained from preclinical experiments using various animals are generally used as references for human studies, it is important to clarify the biochemical properties of CES isozymes. Further experimentation for an understanding of detailed substrate specificity of prodrugs for CES isozymes and its hydrolysates will help us to design the ideal prodrugs.     

Rate conservation principle for discrete-time queues

We present a point-process approach to stationary discrete-time queues where arrivals and services are synchronized. The introduction of a Palm distribution enables us to discuss the ASTA (Arrivals See Time Averages) property, and to derive the rate conservation principle. By applying the principle to the discrete-time queues we present qualitative relationships between customer- and time-stationary distributions, including Little's and Brumelle's formulas.     

Bound diquarks and their Bose–Einstein condensation in strongly coupled quark matter

We explore the formation of diquark bound states and their Bose–Einstein condensation (BEC) in the phase diagram of three-flavor quark matter at nonzero temperature, T, and quark chemical potential, μ  . Using a quark model with a four-fermion interaction, we identify diquark excitations as poles of the microscopically computed diquark propagator. The quark masses are obtained by solving a dynamical equation for the chiral condensate and are found to determine the stability of the diquark excitations. The stability of diquark excitations is investigated in the T–μ$T\text{–}\mu$ plane for different values of the diquark coupling strength. We find that diquark bound states appear at small quark chemical potentials and at intermediate coupling strengths. Bose–Einstein condensation of non-strange diquark states occurs when the attractive interaction between quarks is sufficiently strong.