The Orienteering Problem with Time Windows

The orienteering problem with time windows, denoted by OPTW, belongs to a class of routeing and scheduling problems that arise in physical distribution. It may be modelled as a problem on a graph. It considers a set of nodes (customers), each with an associated profit and service duration (time window), and a set of arcs, each with an associated travel time. The objective of the problem is to construct an acyclic path beginning at a specified origin and ending at a specified destination that maximizes the total profit while observing time window constraints on all nodes and not exceeding a designated time limit. The problem is classified as NP-hard and, thus, an exact algorithm that executes in reasonable computational time is unlikely to exist. Since the problem is highly-constrained, we were able to develop a heuristic (referred to as the ‘tree’ heuristic) based upon an exhaustive search of the feasible solution space. The tree heuristic systematically generates a list of feasible paths and then selects the most profitable path from the list. In comparison with an insertion heuristic, the tree heuristic was found to produce improved values of total profit for heavily-constrained, modest-sized problems with reasonable computational effort.     

A queueing network with a single cyclically roving server

A queueingnetwork that is served by asingle server in a cyclic order is analyzed in this paper. Customers arrive at the queues from outside the network according to independent Poisson processes. Upon completion of his service, a customer mayleave the network, berouted to another queue in the network orrejoin the same queue for another portion of service. The single server moves through the different queues of the network in a cyclic manner. Whenever the server arrives at a queue (polls the queue), he serves the waiting customers in that queue according to some service discipline. Both the gated and the exhaustive disciplines are considered. When moving from one queue to the next queue, the server incurs a switch-over period. This queueing network model has many applications in communication, computer, robotics and manufacturing systems. Examples include token rings, single-processor multi-task systems and others. For this model, we derive the generating function and the expected number of customers present in the network queues at arbitrary epochs, and compute the expected values of the delays observed by the customers. In addition, we derive the expected delay of customers that follow a specific route in the network, and we introduce pseudo-conservation laws for this network of queues.Summary of notation B_i, B _i ^* (s) service time of a customer at queue i and its LST - b_i, b_i ⁽²⁾ mean and second moment of B_i - R_i, R _i ^* (s) duration of switch-over period from queue i and its LST - r_i, r_i mean and second moment of R_i - r, r⁽²⁾ mean and second moment of _i ^N =₁R_i - _i external arrival rate of type-i customers - _i total arrival rate into queue i - _i utilization of queue i; _i=_i - system utilization _i ^N =_1i - c=E[C] the expected cycle length - X _i ^j number of customers in queue j when queue i is polled - X_i=X _i ⁱ number of customers residing in queue i when it is polled - f_i(j) - X _i ^* number of customers residing in queue i at an arbitrary moment - Y_i the duration of a service period of queue i - W_i,T_i the waiting time and sojourn time of an arbitary customer at queue i - F^*(z₁, z₂,..., z_N) GF of number of customers present at the queues at arbitrary moments - F_i(z₁, z₂,..., z_N) GF of number of customers present at the queues at polling instants of queue i - ¯F_i(z₁, z₂,...,z_N) GF of number of customers present at the queues at switching instants of queue i - V_i(z₁, z₂,..., z_N) GF of number of customers present at the queues at service initiation instants at queue i - ¯V_i(z₁,z₂,...,z_N) GF of number of customers present at the queues at service completion instants at queue i The work of this author was supported by the Bernstein Fund for the Promotion of Research and by the Fund for the Promotion of Research at the Technion.Part of this work was done while H. Levy was with AT&T Bell Laboratories.     

Phase transitions of p-type (Pb,Sn,Ge)Te-based alloys for thermoelectric applications

p-type (Pb,Sn,Ge)Te-based alloys for thermoelectric applications were prepared using Bridgman technique. Second-order, rhombohedral to cubic phase transitions are involved, as evaluated from anomalies in the temperature dependence values of Seebeck coefficient, electrical conductivity, heat flow and the elongation, in the vicinity of the phase transition temperature, T_c. The correlation between these anomalies in both the electronic and thermodynamic properties was interpreted by means of the relationship of Fermi energy to the chemical potential (or to the molar Gibbs free energy).     

Scattering from a long helix: Theory and simulation

We consider here the electromagnetic scattering by a long helical particle made from a thin (in comparison to the wavelength) wire. In contrast to several previous theoretical works, we adopt here the algorithm developed for scattering by a multi-layered fiber. In the present work, the helical particle is considered as a hollow cylinder with a thin non-homogeneous membrane for which periodical boundary conditions are imposed.     

Differential response of C57BL/6J mouse and DBA/2J mouse to optic nerve crush

Background  

Retinal ganglion cell (RGC) death is the final consequence of many blinding diseases, where there is considerable variation in the time course and severity of RGC loss. Indeed, this process appears to be influenced by a wide variety of genetic and environmental factors. In this study we explored the genetic basis for differences in ganglion cell death in two inbred strains of mice.     

On Bessel distributions for quasi-split groups

We show that the Bessel distribution attached by Gelfand and Kazhdan and by Shalika to a generic representation of a quasi-split reductive group over a local field is given by a function when it is restricted to the open Bruhat cell. As in the case of the character distribution, this function is real analytic for archimedean fields and locally constant for non-archimidean fields.