Shortest expected delay routing for Erlang servers

The queueing problem with Poisson arrivals and two identical parallel Erlang servers is analyzed for the case of shortest expected delay routing. This problem may be represented as a random walk on the integer grid in the first quadrant of the plane. An important aspect of the random walk is that it is possible to make large jumps in the direction of the boundaries. This feature gives rise to complicated boundary behavior. Generating function approaches to analyze this type of random walk seem to be extremely complicated and have not been successful yet. The approach presented in this paper directly solves the equilibrium equations. It is shown that the equilibrium distribution of the random walk can be written as an infinite linear combination of products. This linear combination is constructed in a compensation procedure. The starting solutions for this procedure are found by solving the shortest expected delay problem with instantaneous jockeying. The results can be used for an efficient computation of performance criteria, such as the waiting time distribution and the moments of the waiting time and the queue lengths.     

A study of charge distributions in inelastic proton-proton collisions

Charge distributions for the secondaries from inelastic proton-proton collisions are studied by means of new data from an experiment at 12 and 24 GeV/c (2 m HBC at CERN). By comparison with π^±p data at 16 GeV/c, the inclusive charge distributions for the fragments of an incident proton and pion, respectively, are analysed. In addition, the cross sections for charge exchange between cms hemispheres are presented for the various charged-particle multiplicities. For events with no more than one neutral particle, charge and baryon exchange between cms hemispheres are compared to those between clusters. For the inelastic two-prong reactions, the two-dimensional distributions in longitudinal phase space are presented.     

On the system of functional equationsf(x + y) = f(x) + f(y) andf(xy) = p (x)f(y) + q(y)f(x)

Aequationes mathematicae -     

Analysis of the reaction pp → p(ππ)0 p,and the question of double pomeron exchange in high-energy production processes

A low-mass S-wave (ππ)⁰ enhancement is observed in the reaction pp → p (ππ)⁰ p at 12 and 24 GeV/c incident momentum. The mechanism for producing these low-mass pion pairs is investigated, and it is shown that double pomeron exchange can contribute at most 5% to their production cross section at 24 GeV/c.     

Photoproduction of neutral pions on hydrogen at photon energies between 200 and 440 MeV

At the Bonn 500 MeV electron synchrotron the differential cross section of the reaction γ+p → π⁰+p has been measured detecting the recoil proton by a magnetic spectrometer. Angular distributions between pion c.m. angles of 50 ° and 160 ° were taken at photon energies between 220 and 420 MeV.     

Aggregation and disaggregation in Markov decision models for inventory control

In this paper the possibility is investigated of using aggregation in the action space for some Markov decision processes of inventory control type. For the standard (s, S) inventory control model the policy improvement procedure can be executed in a very efficient way, therefore, aggregation in the action space is not of much use. However, in situations where the decisions have some aftereffect and, hence, the old decision has to be incorporated in the state, it might be rewarding to aggregate actions. Some variants for aggregation and disaggregation are formulated and analyzed. Numerical evidence is presented.     

Intensity gains with a progressive saturation SPI n.m.r. experiment. The degenerate A—{X3} case

An Ft n.m.r. experiment is described which may lead to a substantial increase in the peak height of n.m.r. signals.