The G/M/1 queue revisited

The G/M/1 queue is one of the classical models of queueing theory. The goal of this paper is two-fold: (a) To introduce new derivations of some well-known results, and (b) to present some new results for the G/M/1 queue and its variants. In particular, we pay attention to the G/M/1 queue with a set-up time at the start of each busy period, and the G/M/1 queue with exceptional first service. Dedicated to Arie Hordijk on his 65th birthday, in friendship and admiration.     

The M/M/c with critical jobs

We consider theM/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.     

Mean value analysis for polling systems

The present paper deals with the problem of calculating mean delays in polling systems with either exhaustive or gated service. We develop a mean value analysis (MVA) to compute these delay figures. The merits of MVA are in its intrinsic simplicity and its intuitively appealing derivation. As a consequence, MVA may be applied, both in an exact and approximate manner, to a large variety of models.     

Shortest expected delay routing for Erlang servers

The queueing problem with Poisson arrivals and two identical parallel Erlang servers is analyzed for the case of shortest expected delay routing. This problem may be represented as a random walk on the integer grid in the first quadrant of the plane. An important aspect of the random walk is that it is possible to make large jumps in the direction of the boundaries. This feature gives rise to complicated boundary behavior. Generating function approaches to analyze this type of random walk seem to be extremely complicated and have not been successful yet. The approach presented in this paper directly solves the equilibrium equations. It is shown that the equilibrium distribution of the random walk can be written as an infinite linear combination of products. This linear combination is constructed in a compensation procedure. The starting solutions for this procedure are found by solving the shortest expected delay problem with instantaneous jockeying. The results can be used for an efficient computation of performance criteria, such as the waiting time distribution and the moments of the waiting time and the queue lengths.     

Approximate analysis of single-server tandem queues with finite buffers

In this paper, we study single-server tandem queues with general service times and finite buffers. Jobs are served according to the Blocking-After-Service protocol. To approximately determine the throughput and mean sojourn time, we decompose the tandem queue into single-buffer subsystems, the service times of which include starvation and blocking, and then we iteratively estimate the unknown parameters of the service times of each subsystem. The crucial feature of this approach is that in each subsystem successive service times are no longer assumed to be independent, but a successful attempt is made to include dependencies due to blocking by employing the concept of Markovian Arrival Processes. An extensive numerical study shows that this approach produces very accurate estimates for the throughput and mean sojourn time, outperforming existing methods, especially for longer tandem queues and for tandem queues with service times with a high variability.     

HTMoL: full-stack solution for remote access,visualization, and analysis of molecular dynamics trajectory data

Research on biology has seen significant advances with the use of molecular dynamics (MD) simulations. The MD methodology enables explanation and discovery of molecular mechanisms in a wide range of natural processes and biological systems. The need to readily share the ever-increasing amount of MD data has been hindered by the lack of specialized bioinformatic tools. The difficulty lies in the efficient management of the data, i.e., in sending and processing 3D information for its visualization. In this work, we present HTMoL, a plug-in-free, secure GPU-accelerated web application specifically designed to stream and visualize MD trajectory data on a web browser. Now, individual research labs can publish MD data on the Internet, or use HTMoL to profoundly improve scientific reports by including supplemental MD data in a journal publication. HTMoL can also be used as a visualization interface to access MD trajectories generated on a high-performance computer center directly. Furthermore, the HTMoL architecture can be leveraged with educational efforts to improve learning in the fields of biology, chemistry, and physics.     

On a generic class of two-node queueing systems

This paper analyzes a generic class of two-node queueing systems. A first queue is fed by an on–off Markov fluid source; the input of a second queue is a function of the state of the Markov fluid source as well, but now also of the first queue being empty or not. This model covers the classical two-node tandem queue and the two-class priority queue as special cases. Relying predominantly on probabilistic argumentation, the steady-state buffer content of both queues is determined (in terms of its Laplace transform). Interpreting the buffer content of the second queue in terms of busy periods of the first queue, the (exact) tail asymptotics of the distribution of the second queue are found. Two regimes can be distinguished: a first in which the state of the first queue (that is, being empty or not) hardly plays a role, and a second in which it explicitly does. This dichotomy can be understood by using large-deviations heuristics. This work has been carried out partly in the Dutch BSIK/BRICKS project.     

格氏试剂衍生-气相色谱-串联质谱法同时测定水果和蔬菜中的三环锡、三苯锡和苯丁锡残留

建立了水果和蔬菜中三环锡、三苯锡和苯丁锡同时检测的格氏试剂衍生-气相色谱-串联质谱方法（GC-MS/MS）。样品经盐酸/四氢呋喃（1：10,v/v）消解,正己烷振荡提取,乙基溴化镁衍生和Florisil固相萃取净化,采用GC-MS/MS多反应监测（MRM）模式对3种有机锡化合物进行定性和定量分析。实验结果表明,以苹果为代表性样品基质,三环锡、三苯锡和苯丁锡的检出限（LOD）分别为2.0、1.5和3.4 μg/kg （以Sn计）,在10、20、50、200 μg/kg （以Sn计）共4个添加水平下的平均回收率为72.4%~107.1%,相对标准偏差为0.4%~14.2%。该方法灵敏度高,选择性强,可以实现3种有机锡农药的同时检测,能够满足国内外残留限量的检测要求。     

A product form solution to a system with multi-type jobs and multi-type servers

We consider a memoryless single station service system with servers \(\mathcal{S}=\{m_{1},\ldots,m_{K}\}\), and with job types \(\mathcal{C}=\{a,b,\ldots\}\). Service is skill-based, so that server m _i can serve a subset of job types \(\mathcal{C}(m_{i})\). Waiting jobs are served on a first-come-first-served basis, while arriving jobs that find several idle servers are assigned to a feasible server randomly. We show that there exist assignment probabilities under which the system has a product-form stationary distribution, and obtain explicit expressions for it. We also derive waiting time distributions in steady state.