The M/M/c with critical jobs

We consider the M/M/c queue, where customers transfer to a critical state when their queueing (sojourn) time exceeds a random time. Lower and upper bounds for the distribution of the number of critical jobs are derived from two modifications of the original system. The two modified systems can be efficiently solved. Numerical calculations indicate the power of the approach

Disability in the Workplace in China: Situation Assessment

A compelling argument can be made that employment of people with disabilities should be gaining recognition as an underutilized weapon in the talent wars of Asia. One has only to look at the proportion of people with disabilities that make up our communities, the continuing employment disparities that people with disabilities continue to face and the resulting high levels of poverty for this population – up against the talent shortages in fast-growth markets across the region. As China’s skewed demographic dynamics become increasingly apparent, resulting in a rapidly aging population and a diminishing supply of workforce entrants, an increasing share of the workforce will include older employees with disabilities, necessitating a fundamental change in workplace practices involving people with disabilities, as well as a greater need to look at persons with disabilities as a potential source of talent. Although China has created a broad legislative framework to protect the right to work for persons with disabilities, it lacks specificity and clear measures of enforcement, as evidenced in continued employment marginalization, poor educational outcomes, and thus higher poverty levels of persons with disabilities. To further understanding of workforce inclusion of persons with disabilities in China, and to identify practical ways forward for employers, The Conference Board China Center and the K. Lisa Yang and Hock E. Tan Institute on Employment and Disability (YTI) at Cornell University’s ILR School partnered to explore how companies can tap the talent pool of people with disabilities and improve their employment outcomes. The scope of the research encompassed a series of interviews with disability rights-focused NGOs in China, a detailed literature review, a comprehensive review of China’s regulatory framework supporting employment for persons with disabilities, and a detailed assessment of the demographics of disability and the status of people with disabilities in China such as prevalence rates, access to education, employment disparities and resulting poverty and household income rates. This report draws from the broader research findings and provides business practitioners with an overview of the current situation, challenges, and root causes of employment barriers for persons with disabilities in China. To complement this work, The China Center and YTI convened a practitioner roundtable in Beijing in September 2018. Participants explored in detail how the official, publicly available data on living and working conditions of persons with disabilities compare to actual experiences of employers in China, whether companies are actively recruiting disabled workers, what the internal and external obstacles are to recruitment, and what the impact of the government quota system is, for good or for bad. A separate report on this roundtable is also availabl

The Mass Dependence of Stellar Rotation in the Orion Nebula Cluster

We have determined new rotation periods for 404 stars in the Orion Nebula Cluster using the Wide Field Imager attached to the MPG/ESO 2.2 m telescope on La Silla, Chile. Mass estimates are available for 335 of these and most have M < 0.3 M_sun. We confirm the existence of a bimodal period distribution for the higher mass stars in our sample and show that the median rotation rate decreases with increasing mass for stars in the range 0.1 < M <0.4 M_sun. While the spread in angular momentum (J) at any given mass is more than a factor of 10, the majority of lower mass stars in the ONC rotate at rates approaching 30% of their critical break-up velocity, as opposed to 5-10% for solar-like stars. This is a consequence of both a small increase in observed specific angular momentum (j=J/M) and a larger decrease in the critical value of j with decreasing mass. Perhaps the most striking fact, however, is that j varies by so little - less than a factor of two - over the interval 0.1-1.0 M_sun. The distribution of rotation rates with mass in the ONC (age ~ 1 My) is similar in nature to what is found in the Pleiades (age ~ 100 My). These observations provide a significant new guide and test for models of stellar angular momentum evolution during the proto-stellar and pre-main sequence phases.Comment: 11 pages, 3 figure

Stuck in the slow lane: reconceptualising the links between gender, transport and social exclusion

This article draws upon primary research undertaken with over 3,000 women in the North East of England to explore the links between women, transport and the labour market. The research, funded by the ESF, advances the idea of spatiality as a social construction and builds on seminal studies relating to women and poverty to consider the way in which a gender division of transport constrains women's mobility and restricts their employment opportunities. It is likely to contribute to important debates, concerning strategies to tackle worklessness and the most effective spatial level at which to configure public transport networks

On the rate of convergence to stationarity of the M/M/N queue in the Halfin-Whitt regime

We prove several results about the rate of convergence to stationarity, that is, the spectral gap, for the M/M/n queue in the Halfin-Whitt regime. We identify the limiting rate of convergence to steady-state, and discover an asymptotic phase transition that occurs w.r.t. this rate. In particular, we demonstrate the existence of a constant $B^*\approx1.85772$ s.t. when a certain excess parameter $B\in(0,B^*]$, the error in the steady-state approximation converges exponentially fast to zero at rate $\frac{B^2}{4}$. For $B>B^*$, the error in the steady-state approximation converges exponentially fast to zero at a different rate, which is the solution to an explicit equation given in terms of special functions. This result may be interpreted as an asymptotic version of a phase transition proven to occur for any fixed n by van Doorn [Stochastic Monotonicity and Queueing Applications of Birth-death Processes (1981) Springer]. We also prove explicit bounds on the distance to stationarity for the M/M/n queue in the Halfin-Whitt regime, when $B<B^*$. Our bounds scale independently of $n$ in the Halfin-Whitt regime, and do not follow from the weak-convergence theory.Comment: Published in at http://dx.doi.org/10.1214/12-AAP889 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Strategies for a centralized single product multiclass M/G/1 make-to-stock queue

Make-to-stock queues are typically investigated in the M/M/1 settings. For centralized single-item systems with backlogs, the multilevel rationing (MR) policy is established as optimal and the strict priority (SP) policy is a practical compromise, balancing cost and ease of implementation. However, the optimal policy is unknown when service time is general, i.e., for M/G/1 queues. Dynamic programming, the tool commonly used to investigate the MR policy in make-to-stock queues, is less practical when service time is general. In this paper we focus on customer composition: the proportion of customers of each class to the total number of customers in the queue. We do so because the number of customers in M/G/1 queues is invariant for any nonidling and nonanticipating policy. To characterize customer composition, we consider a series of two-priority M/G/1 queues where the first service time in each busy period is different from standard service times, i.e., this first service time is exceptional. We characterize the required exceptional first service times and the exact solution of such queues. From our results, we derive the optimal cost and control for the MR and SP policies for M/G/1 make-to-stock queues

Online Makespan Minimization with Parallel Schedules

In online makespan minimization a sequence of jobs $\sigma = J_1,..., J_n$ has to be scheduled on $m$ identical parallel machines so as to minimize the maximum completion time of any job. We investigate the problem with an essentially new model of resource augmentation. Here, an online algorithm is allowed to build several schedules in parallel while processing $\sigma$. At the end of the scheduling process the best schedule is selected. This model can be viewed as providing an online algorithm with extra space, which is invested to maintain multiple solutions. The setting is of particular interest in parallel processing environments where each processor can maintain a single or a small set of solutions. We develop a (4/3+\eps)-competitive algorithm, for any 0<\eps\leq 1, that uses a number of 1/\eps^{O(\log (1/\eps))} schedules. We also give a (1+\eps)-competitive algorithm, for any 0<\eps\leq 1, that builds a polynomial number of (m/\eps)^{O(\log (1/\eps) / \eps)} schedules. This value depends on $m$ but is independent of the input $\sigma$. The performance guarantees are nearly best possible. We show that any algorithm that achieves a competitiveness smaller than 4/3 must construct $\Omega(m)$ schedules. Our algorithms make use of novel guessing schemes that (1) predict the optimum makespan of a job sequence $\sigma$ to within a factor of 1+\eps and (2) guess the job processing times and their frequencies in $\sigma$. In (2) we have to sparsify the universe of all guesses so as to reduce the number of schedules to a constant. The competitive ratios achieved using parallel schedules are considerably smaller than those in the standard problem without resource augmentation