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61.
We develop power series approximations for a discrete-time queueing system with two parallel queues and one processor. If
both queues are nonempty, a customer of queue 1 is served with probability β, and a customer of queue 2 is served with probability 1−β. If one of the queues is empty, a customer of the other queue is served with probability 1. We first describe the generating
function U(z
1,z
2) of the stationary queue lengths in terms of a functional equation, and show how to solve this using the theory of boundary
value problems. Then, we propose to use the same functional equation to obtain a power series for U(z
1,z
2) in β. The first coefficient of this power series corresponds to the priority case β=0, which allows for an explicit solution. All higher coefficients are expressed in terms of the priority case. Accurate approximations
for the mean stationary queue lengths are obtained from combining truncated power series and Padé approximation. 相似文献
62.
O.J. Boxma 《Stochastic Processes and their Applications》1978,8(1):93-100
This paper considers the supremum m of the service times of the customers served in a busy period of the M?G?1 queueing system. An implicit expression for the distribution m(w) of m is derived. This expression leads to some bounds for m(w), while it can also be used to obtain numerical results. The tail behaviour of m(w) is investigated, too. The results are particularly useful in the analysis of a class of tandem queueing systems. 相似文献
63.
Theoretical calculations at the DFT (B3LYP) level have been undertaken on tris- and bis(boryl) complexes. Two model d(6) complexes [Rh(PH(3))(3)(BX(2))(3) and Rh(PH(3))(4)(BX(2))(2)(+), X = OH and H] have been studied. In the model tris(boryl) complex (X = OH) we find a fac structure as a minimum, in accordance with the experimental data. The mer geometries are found to be higher in energy. Analysis of the energetic ordering in mer isomers shows that back-bonding in these complexes involves a bonding Rh-B orbital (and not a d-block orbital as usual). This surprising behavior is rationalized through a qualitative MO analysis and quantitative NBO analysis. Results on the bis(boryl) complex confirm the preceding analysis. Full optimization of unsubstituted (X = H) complexes leads to structures in which the BH(2) moieties are coupled. In the optimal geometry of the bis(boryl) complex, the B(2)H(4) ligand resembles the transition state of the C(2v)-->D(2d) interconversion of the isolated B(2)H(4) species. In the tris(boryl) complex, we find a B(3)H(6) ligand in which the B(3) atoms define an isosceles triangle with one hydrogen bridging the shorter B-B bond. 相似文献
64.
65.
We consider a class of two-queue polling systems with exhaustive service, where the order in which the server visits the queues is governed by a discrete-time Markov chain. For this model, we derive an expression for the probability generating function of the joint queue length distribution at polling epochs. Based on these results, we obtain explicit expressions for the Laplace–Stieltjes transforms of the waiting-time distributions and the probability generating function of the joint queue length distribution at an arbitrary point in time. We also study the heavy-traffic behaviour of properly scaled versions of these distributions, which results in compact and closed-form expressions for the distribution functions themselves. The heavy-traffic behaviour turns out to be similar to that of cyclic polling models, provides insights into the main effects of the model parameters when the system is heavily loaded, and can be used to derive closed-form approximations for the waiting-time distribution or the queue length distribution. 相似文献
66.
Onno L.J. Gijzeman 《Chemical physics letters》1974,26(2):152-156
The non-diagonal matrix elements in the adiabatic Born-Oppenheimer approximation are considered. The effect of the Q-dependence of the electronic energy denominator is calculated explicitly for an arbitrary initial and final state. It is shown that the inclusion of this effect does not change the relative values of the coupling matrix elements for different initial vibronic states. 相似文献
67.
In this note we consider two queueing systems: a symmetric polling system with gated service at allN queues and with switchover times, and a single-server single-queue model with one arrival stream of ordinary customers andN additional permanently present customers. It is assumed that the combined arrival process at the queues of the polling system coincides with the arrival process of the ordinary customers in the single-queue model, and that the service time and switchover time distributions of the polling model coincide with the service time distributions of the ordinary and permanent customers, respectively, in the single-queue model. A complete equivalence between both models is accomplished by the following queue insertion of arriving customers. In the single-queue model, an arriving ordinary customer occupies with probabilityp
i
a position at the end of the queue section behind theith permanent customer,i = l, ...,N. In the cyclic polling model, an arriving customer with probabilityp
i
joins the end of theith queue to be visited by the server, measured from its present position.For the single-queue model we prove that, if two queue insertion distributions {p
i, i
= l, ...,N} and {q
i, i
= l, ...,N} are stochastically ordered, then also the workload and queue length distributions in the corresponding two single-queue versions are stochastically ordered. This immediately leads to equivalent stochastic orderings in polling models.Finally, the single-queue model with Poisson arrivals andp
1 = 1 is studied in detail.Part of the research of the first author has been supported by the Esprit BRA project QMIPS. 相似文献
68.
Inspired by a problem regarding cable access networks, we consider a two station tandem queue with Poisson arrivals. At station 1 we operate a gate mechanism, leading to batch arrivals at station 2. Upon arrival at station 1, customers join a queue in front of a gate. Whenever all customers present at the service area of station 1 have received service, the gate before as well as a gate behind the service facility open. Customers leave the service area and enter station 2 (as a batch), while all customers waiting at the gate in front of station 1 are admitted into the service area. For station 1 we analyse the batch size and the time between two successive gate openings, as well as waiting and sojourn times of individual customers for different service disciplines. For station 2, we investigate waiting times of batch customers, where we allow that service times may depend on the size of the batch and also on the interarrival time. In the analysis we use Wiener–Hopf factorization techniques for Markov modulated random walks. 相似文献
69.
Queueing Systems - The workload of a generalized n-site asymmetric simple inclusion process (ASIP) is investigated. Three models are analyzed. The first model is a serial network for which the... 相似文献
70.
In this paper we derive a technique for obtaining limit theorems for suprema of Lévy processes from their random walk counterparts. For each a>0, let $\{Y^{(a)}_{n}:n\ge1\}In this paper we derive a technique for obtaining limit theorems for suprema of Lévy processes from their random walk counterparts.
For each a>0, let {Y(a)n:n 3 1}\{Y^{(a)}_{n}:n\ge1\} be a sequence of independent and identically distributed random variables and {X(a)t:t 3 0}\{X^{(a)}_{t}:t\ge0\} be a Lévy process such that X1(a)=dY1(a)X_{1}^{(a)}\stackrel{d}{=}Y_{1}^{(a)},
\mathbbEX1(a) < 0\mathbb{E}X_{1}^{(a)}<0 and
\mathbbEX1(a)-0\mathbb{E}X_{1}^{(a)}\uparrow0 as a↓0. Let S(a)n=?k=1n Y(a)kS^{(a)}_{n}=\sum _{k=1}^{n} Y^{(a)}_{k}. Then, under some mild assumptions, , for some random variable and some function Δ(⋅). We utilize this result to present a number of limit theorems for suprema of Lévy processes in the
heavy-traffic regime. 相似文献