Refining Cosmetatos' Approximation for the Mean Waiting Time in the M/D/s Queue

This paper deals with refining Cosmetatos's approximation for the mean waiting time in an M/D/s queue. Although his approximation performs quite well in heavy traffic, it overestimates the true value when the number of servers is large or the traffic is light. We first focus on a normalized quantity that is a ratio of the mean waiting times for the M/D/s and M/M/s queues. Using some asymptotic properties of the quantity, we modify Cosmetatos's approximation to obtain better accuracy both for large s and in light traffic. To see the quality of our approximation, we compare it with the exact value and some previous approximations. Extensive numerical tests indicate that the relative percentage error is less than 1% for almost all cases with s ≤ 20 and at most 5% for other cases.     

Approximating the Mean Waiting Time in the <Emphasis Type="Italic">GI/G/s</Emphasis> Queue

We provide two distribution-dependent approximations for the mean waiting time in a GI/G/s queue. Both approximations are weighted combinations of the exact mean waiting times for the GI/M/s and M/D/s queues each of which has the same mean service time and traffic intensity as in the approximating GI/G/s queue. The weights in the approximations are expressed by the service-time c.d.f. and the first two moments of interarrival and service times. To examine the performance of our approximations, they are numerically compared with exact solutions and previous two-moment approximations for various cases. Extensive numerical comparisons indicate that the relative percentage errors of the approximations are of the order of 5% in moderate traffic and 1% in heavy traffic, except for extreme cases.     

A novel asymmetrical phosphine tetracobalt complex ofo-Mercaptophenol: Synthesis,structure, and properties of Co4mp4(Hmp)(PBu 3 n )3 (H2mp=o-Mercaptophenol)

Complex Co₄mp₄(Hmp)(PBu ₃ ⁿ )₃ (1) (H₂mp=o-Mercaptophenol) was obtained from the reaction of CoCl₂ and H₂mp in the presence of PBu ⁿ ₃ and NaOMe with restricted oxidation. X-ray crystallographic data: triclinic, space group ,a=15.657(5) Å,b=20.469(8) Å,c=12.383(3) Å,=93.59(3)°, =112.45(2)°, =93.65(3)°,V=3648.7 ų,Z=2,D _c =1.33 g/cm³;R=0.065. The molecule consists of four cobalt atoms unsymmetrically bridged by S or S and O atoms from four of the five mp ligands. The fifth mp is terminally chelated to Co(4) which is in a distorted trigonal bipyramidal geometry, while Co(1)-Co(3) are square pyramidal. Atom Co(2) is bonded to Co(1) and Co(3) (average distance 2.632 Å) with strong interactions while Co(4) is only loosely connected to Co(1) (3.402 Å) and Co(3) (2.956 Å) through oxygen bridges and a hydrogen bond. The different coordination environments O₂S₂P, S₄P, and O₄S of the cobalt atoms make the molecule highly asymmetrical. XPS fitting data confirm the difference of the Co atoms. FABMS data indicate the possible fragmentation routes. The complex is paramagnetic with _eff=5.2 _B.     

Experiments in Solving Mixed Integer Programming Problems on a Small Array of Transputers

The time-consuming process of solving large-scale Mixed Integer Programming problems using the branch-and-bound technique can be speeded up by introducing a degree of parallelism into the basic algorithm. This paper describes the development and implementation of a parallel branch-and-bound algorithm created by adapting a commercial MIP solver. Inherent in the design of this software are certain ad hoc methods, the use of which are necessary in the effective solution of real problems. The extent to which these ad hoc methods can successfully be transferred to a parallel environment, in this case an array of at most nine transputers, is discussed. Computational results on a variety of real integer programming problems are reported.     

Approximate analytic theory of the multijunction grill

A general approximate analytic theory of the multijunction grill is developed. Omitting the evanescent modes in the subsidiary waveguides both at the junction and at the grill mouth and neglecting multiple wave reflection between the same places we derive simple formulae for the reflection coefficient, the amplitudes of the incident and reflected waves and the spectral power density. All these quantities are expressed through the basic grill parameters (the electric length of the structure and the phase shift between adjacent waveguides) and two sets of the reflection coefficients describing wave reflections in the subsidiary waveguides at the junction and at the mouth. The approximate expressions for these coefficients are also given. The results are compared with numerical solution of two specific examples and they prove to be useful for the optimization and design of the multijunction grills. For the JET structure, which is composed of multijunction sections, it is shown that, in the case of the dense plasma, many results can be obtained from the simple formulae for two-waveguide multijunction grill.A part of this work was done at the stay of the second author in the Joint Institute of Nuclear Research in Dubna and he wishes to thank that Institution for hospitality.     

Univariate Stochastic Programming with Random Decision Variable

The problem of minimising E(X) subject to the constraints X ? 0, P(X ? b) ? a(0 < a < 1) has been considered, where b is a non-negative random variable with continuous probability distribution. A necessary and sufficient condition for randomised decisions to be superior to the non-randomised one has been derived.