A queueing system with multiple service time distributions

This paper explores a modification of the output discipline for the Poisson input, exponential output, single channel, first-come, first-served queueing system. Instead, the service time distribution of customers beginning service when alone in the system is considered different from that governing service times of all other customers. More specifically, the service times of lone customers are governed by a one parameter gamma distribution, while the service times of all other customers are exponentially ajstributed. The generating function for the steady-state probsbilities, n_j = Pr { j customers in system at an arbitrary point of departure}, of the imbedded chain, {X_n/X_n = number in system after nth customer is serviced}, is obtained, and the steady-state probabilities, themselves, are found in closed form.     

Queues with stochastic service rates

The purpose of this paper is to explore an extension of the output discipline for the Poisson input, general output, single channel, first-come, first-served queueing system. The service time parameter, μ, is instead considered a random variable, M. In other words, the service time random variable, T, is to be conditioned by a parameter random variable, M. Therefore, if the distribution function of M is denoted by F_M(μ) and the known conditional service time distribution as B(t |_μ), then the unconditional service distribution is given by B(t) = Pr {T ≤ t}. = ∫_-∞^∞ B(t |_μ) dF_M(μ). Results are obtained that characterize queue size and waiting time using the imbedded Markov chain approach. Expressions are derived for the expected queue length and Laplace-Stieltjes transforms of the steady-state waiting time when conditional service times are exponential. More specific results are found for three special distributions of M: (1) uniform on [1.2]; (2) two-point; and (3) gamma.     

Use of completely reduced matrices in solving transportation problems with fixed charges

This paper shows how completely reduced matrices can be used in obtaining exact or approximate solutions to transportation problems with fixed charges. It does not treat methods for obtaining reduced matrices, which are available elsewhere, but it does discuss the problem of obtaining a completely reduced matrix, and then a general parametric solution to the primal problem, from any particular solution. Methods for obtaining particular solutions with determinacies of maximum order (solutions for the constant fixed charges problem) are then presented. The paper terminates with a discussion of methods which are useful in obtaining approximations to solutions of fixed charges problems with charges not constant.     

NATO’s push into the Caucasus: geopolitical flashpoints and limits for expansion

The Caucasus has been a major flashpoint of contention between NATO and a resurgent Russia since the collapse of the Soviet Union. The rivalry saw the escalation of hostility in the region during the brief 2008 Russo-Georgian War where a NATO-backed Georgia challenged South Ossetia supported by the Russian military. In 2011, NATO officially recognised Georgia as a potential member, challenging Russia’s traditional sphere of influence in the Caucasus. Moscow says the Eastward expansion of NATO into the Baltics and to include Georgia as a member state is a method of containing a resurgent Russia. However, the former Soviet Republics of Ukraine, the Baltics and Georgia, maintain that Russia represents a threat to their sovereignty, as seen by the Russian support of the breakaway unrecognised Republics of South Ossetia and Abkhazia. A hostile rivalry between the Russian-backed Armenia and Azerbaijan, which is reliant upon NATO-member Turkey, intensifies the polarisation in the Caucasus.     

Multi-item service constrained (s,S) policies for spare parts logistics systems

Many organizations providing service support for products or families of products must allocate inventory investment among the parts (or, identically, items) that make up those products or families. The allocation decision is crucial in today's competitive environment in which rapid response and low levels of inventory are both required for providing competitive levels of customer service in marketing a firm's products. This is particularly important in high-tech industries, such as computers, military equipment, and consumer appliances. Such rapid response typically implies regional and local distribution points for final products and for spare parts for repairs. In this article we fix attention on a given product or product family at a single location. This single-location problem is the basic building block of multi-echelon inventory systems based on level-by-level decomposition, and our modeling approach is developed with this application in mind. The product consists of field-replaceable units (i.e., parts), which are to be stocked as spares for field service repair. We assume that each part will be stocked at each location according to an (s, S) stocking policy. Moreover, we distinguish two classes of demand at each location: customer (or emergency) demand and normal replenishment demand from lower levels in the multiechelon system. The basic problem of interest is to determine the appropriate policies (s_i S_i) for each part i in the product under consideration. We formulate an approximate cost function and service level constraint, and we present a greedy heuristic algorithm for solving the resulting approximate constrained optimization problem. We present experimental results showing that the heuristics developed have good cost performance relative to optimal. We also discuss extensions to the multiproduct component commonality problem.     

Evaluation of base-stock policies in multiechelon inventory systems with compound-poisson demands

This article analyzes a model of a multiechelon inventory system: The exogenous demands form independent compound-Poisson processes. Each location follows a base-stock policy. The transit times between locations may be stochastic. Instead of assuming independent transit times, we follow an approach closer to the standard treatment of single-location models. We develop procedures to compute steady-state performance measures, including average backorders and average inventories. The model and the analysis generalize those of Svoronos and Zipkin, who treat the case of pure Poisson demands.     

Graveyard of Analogies: The Use and Abuse of History for the War in Afghanistan

Decades of scholarship have warned against using historical analogies for policymaking. But the Taliban insurgency appears, on the surface, to confirm the usefulness of historical analogies to the British and Soviet wars in Afghanistan. I review the use of analogies for the war in Afghanistan and argue the analogies were historically unsound and strategically unhelpful. In fact, their effect on policy helped create the conditions for the very insurgency policymakers most hoped to avoid. The Taliban insurgency did not occur because of the presence of too many foreign troops and aid workers, but because there were too few.     

Cinema,drone warfare and the framing of counter-terrorism

The study of the cinematic representation is extremely useful in framing of counter-terrorism policies, whether in the US or elsewhere. This paper examines cinema’s interest in drone warfare as well as the lives and personalities of drone pilots. It argues that drone warfare suffers a considerable image problem that has been brought out in several recent features and it is unlikely that any major cinematic myth of drone warfare will easily develop, certainly in comparison to myths concerning special forces and special operations.     

Portfolio analysis for defense: taking account of networking

To manage their assets at an enterprise level, defense organizations have turned to portfolio theory for the planning, analysis and management of their military forces and materiel. Despite being well established in the commercial sector, the application of portfolio approaches in defense is problematic. The vexatious question for defense of how to define and measure benefits arising is complicated by the increased utility and effectiveness achieved through networking of military forces and the equipment they use. The authors discuss the challenges for defense in using a portfolio approach and propose a conceptual model for dealing with the effects arising from networking with information and communications technologies.