An M/M/1 queue with delayed feedback

We present some results for M/M/1 queues with finite capacities with delayed feedback. The delay in the feedback to an M/M/1 queue is modelled as another M-server queue with a finite capacity. The steady state probabilities for the two dimensional Markov process {N(t), M(t)} are solved when N(t) = queue length at server 1 at t and M(t) = queue length at server 2 at t. It is shown that a matrix operation can be performed to obtain the steady state probabilities. The eigenvalues of the operator and its eigenvectors are found. The problem is solved by fitting boundary conditions to the general solution and by normalizing. A sample problem is run to show that the solution methods can be programmed and meaningful results obtained numerically.     

Use of discounted force arrivals in static force comparisons

In traditional static comparisons of two opposing forces, weapons systems on each side are added together after weighting them according to a weapon scoring system. The scoring system does not reflect the availability times of the weapon systems in a perceived conflict. In this paper it is suggested how availability times can be incorporated by introducing the net present value of force arrival patterns. The concept is extended to include the case where uncertainty concerning warning time is reflected through a probability distribution for the time of outbreak of hostilities.     

Quasi-separable utility functions

This paper is concerned with a method for the assessment of utility functions of multi-numeraire consequences. It is proven that given von Neumann and Morgenstern's axioms of “rational behavior” and two additional assumptions, the utility function for (x, y) consequences can be written as U(x, y) = U_x(x) + U_y(y) + KU_x(x) U_y(y). K is a constant that must be evaluated empirically. This form shall be designated as a quasi-separable utility function. It is more general than the separable utility function and is shown to be nearly as easy to use. Implications and ramifications of such a utility function and its requisite assumptions are discussed. A technique for practical application of this work is presented.     

Enmeshed in insurgency: Britain's protracted retreats from Iraq and Afghanistan

Ten years of counterinsurgency in Iraq and Afghanistan have produced little in Britain's national interest. This article examines the political objectives set in these wars and the reasons why they have proved elusive. The core foreign policy aim was to sustain Britain's position as a great power by assuming responsibility for global order. Alliances with the United States and NATO would be the diplomatic tool for pursuing this aim. These alliances brought obligations, in the shape of agreed common threats. Rogue regimes with weapons of mass destruction and international terrorists harboured in failed states were deemed the primary threats to British security. Military means were therefore used in Iraq and Afghanistan to attack them. Whether Tony Blair's vision of global order ever made sense is debatable, and it attracted scepticism from the outset. The article argues experience in Iraq and Afghanistan showed that a strategy to eliminate terrorism (the WMD threat turned out never to have existed) by expeditionary counterinsurgency could only fail. Therefore the attention lavished on operational-level performance by most studies is misplaced, because no amount of warfighting excellence could make up for strategic incoherence. Finally, the article proposes the more important question arising from the last ten years is why the UK pursued a futile strategy for so long. The difficulties associated with interpreting events, a malfunctioning strategic apparatus, weak political oversight, and bureaucratic self-interest are posited as the most significant explanations.     

Cycles and trends in the procurement system: Anticipating changes in acquisition legislation, regulation and policy

In conclusion, let me raise the question of whether the Law Panel can impact these cycles or reverse these trends. If they are regarded as historical imperatives, the answer is clearly No. But we have been urged to be bold and to try to devise a new, simplified statute that will take us back to a better day. We are going to do that, without regard to the question whether Congress will accept the solution.

There probably has never been a better time for the Panel's report than the present; the window of opportunity is open. But what the Panel recommends is going to be awfully hard to sell, even in a window-of-opportunity year. If the predictions come true about the defense budget's going down to the level of the period when Eisenhower remained a Major for 14 years, maybe Congress will be receptive to anything that adds a little bit of value to the defense dollar. With this in mind, the Law Panel is likely to be very bold in its attempt to streamline the procurement system and reduce oversight. Hope springs eternal . . . .     

The M/G/1 queue with instantaneous bernoulli feedback

In this paper we are concerned with several random processes that occur in M/G/1 queues with instantaneous feedback in which the feedback decision process is a Bernoulli process. Queue length processes embedded at various times are studied. It is shown that these do not all have the same asymptotic distribution, and that in general none of the output, input, or feedback processes is renewal. These results have implications in the application of certain decomposition results to queueing networks.     

Western drones and African security

While unmanned aerial vehicles (UAVs) have become a standard element of modern armed forces, African countries have been reluctant to acquire remotely piloted aircraft for military purposes until recently. This is mainly due to a lack of industrial capabilities and, for military purposes so far, procurement policies that have concentrated on small arms and light weapons, more prestigious armoured vehicles and combat aircraft. Moreover, counter-insurgency strategies in Africa tend to focus on manoeuvre warfare, co-opting rebels or fighting them using armed proxies. As a consequence, international counterterrorism operations against fanatical and reckless groups like al-Qaeda in the Islamic Maghreb and Boko Haram in sub-Saharan Africa are characterised by a strong dependence on Western forces providing UAV-based reconnaissance and, in some cases for the United States, military strikes by drones. This essay reviews some of the incentives and problems of the use of UAVs in the African context. Given the geographical and military conditions of asymmetric warfare in Africa, and potential problems concerning international law, ethical aspects of the use of arms, and civil–military relations notwithstanding, it is argued that African security forces should develop their own UAV capabilities by intensifying their cooperation with Western armed forces.     

An Investigation of the Weights of Pattern 1907 Bayonets made in the UK around the First World War Period

The standard issue bayonet of the British Army immediately preceding and during the First World War was the Pattern 1907. This was manufactured at different times and in varying numbers during that period by one official body, the Royal Small Arms Factory at Enfield, and by five private contractors. These bayonets were made according to published official specifications issued by the War Department and based on a ‘pattern example’ provided by the Royal Small Arms Factory. The specifications indicate, inter alia, the quality of metal used in making the bayonets, methods of inspection and proofing, and the required maximum and minimum weight range of the completed bayonet. However, examination of a series of these bayonets in a private collection suggested that their weights varied considerably from the mid-point values of the allowed weight ranges in the original and amended specifications (16.5 oz. and 17 oz., respectively). To establish if this was a common feature among this class of bayonet as opposed to a chance factor, the weights of other surviving Pattern 1907 bayonets were determined and compared to establish the degree of variance from the official specifications as originally set out by the Royal Small Arms Factory. Seventy-six percent of the 142 bayonets surveyed were found to be above the mid-point of the allowed weight range given in the amended manufacturing specifications, with many being at the upper end of the allowed range. This is a statistically unusual result. It is speculated that the target weight may have been deliberately set higher by the individual manufacturers to eliminate the possibility of rejection of any underweight bayonets by the Royal Small Arms Factory inspectors and so a refusal of acceptance and payment for the work.