The queue G/M/m/N: Busy period and cycle,waiting time under reverse and random order service

The busy period, busy cycle, and the numbers of customers served and lost therein, of the G/M/m queue with balking is studied via the embedded Markov chain approach. It is shown that the expectations of the two discrete variables give the loss probability. For the special case G/M/1/N a closed expression in terms of contour integrals is obtained for the Laplace transform of these four variables. This yields as a byproduct the LIFO waiting time distribution for the G/M/m/N queue. The waiting time under random order service for this queue is also studied.     

Experimental and numerical investigations of interface properties of Ti6Al4V/CP-Ti/Copper composite plate prepared by explosive welding

Explosive welding technique is widely used in many industries. This technique is useful to weld different kinds of metal alloys that are not easily welded by any other welding methods. Interlayer plays an important role to improve the welding quality and control energy loss during the collision process. In this paper, the Ti6Al4V plate was welded with a copper plate in the presence of a commercially pure titanium interlayer. Microstructure details of welded composite plate were observed through optical and scanning electron microscope. Interlayer-base plate interface morphology showed a wavy structure with solid melted regions inside the vortices. Moreover, the energy dispersive spectroscopy analysis in the interlayer-base interface reveals that there are some identified regions of different kinds of chemical equilibrium phases of Cu–Ti, i.e. CuTi, Cu₂Ti, CuTi₂, Cu₄Ti, etc. To study the mechanical properties of composite plates, mechanical tests were conducted, including the tensile test, bending test, shear test and Vickers hardness test. Numerical simulation of explosive welding process was performed with coupled Smooth Particle Hydrodynamic method, Euler and Arbitrary Lagrangian-Eulerian method. The multi-physics process of explosive welding, including detonation, jetting and interface morphology, was observed with simulation. Moreover, simulated plastic strain, temperature and pressure profiles were analysed to understand the welding conditions. Simulated results show that the interlayer base plate interface was created due to the high plastic deformation and localized melting of the parent plates. At the collision point, both alloys behave like fluids, resulting in the formation of a wavy morphology with vortices, which is in good agreement with the experimental results.     

Nigerian women and the trends of kidnapping in the era of Boko Haram insurgency: patterns and evolution

ABSTRACT

The rising trend of kidnapping targeting women has shown that counterinsurgency does not begin and end with the strategic advantage of state security providers in the security market and the field. Kidnapping of females by Boko Haram insurgents threatens human security and hinders sustainable development goals in Northeastern Nigeria. With primary and secondary sources, this qualitative study examines how Boko Haram insurgents target women in Northeastern Nigeria. The paper argues that community driven security strategy achievable through the collaboration between state and traditional security providers, can prevent the entry and easy escape of the insurgents. It concludes that the forces of order should sustain a policy of stop and searches until insurgents are defeated along with a programme of community-based human rights education and insurgency emergency response system for quick response to security threats.