GI／G／1系统队长的极限分布

关于GI／G／1排队系统队长的极限分布存在的一个充分条件被建立．     

M／M／1／k后馈系统中的随机过程

本文对Ｍ／Ｍ／１／ｋ后馈排队系统中各随机过程的Ｐｏｉｓｓｏｎ性进行了讨论，推广了Ｂｒｅｍａｕｄ（［２］，［３］）的相应结果。所得结论表明Ｍ／Ｍ／１／ｋ后馈系统与Ｍ／Ｍ／１后馈系统情况有所不同，即在某些情况下，除总输出过程外，还有其它的过程也可能是Ｐｏｉｓｓｏｎ过程。顺便又地Ｍ／Ｍ／Ｃ／ｋ前馈后馈排队系统的动态数学模型进行了严格的讨论。     

PH／PH／1／N反馈排队系统的逼留时间

具有反馈依赖于队长的ＰＨ／ＰＨ／１／Ｎ排队系统的队长和忙期的研究已在文（１）中解决，本文主要解决本系统的逗留时间的研究。     

截超泊松排队:具有阻碍、放弃和不同服务员H_k/M/2/N系统(英文)

本文讨论具有阻碍、放弃，不同服务员Ｋｋ／Ｍ／２／Ｎ排队系统的解析解．对经典的一种先入先出的修改排队规则在较一般的条件下被采用了，得到了稳态概率和一些有效度量的显式．一些特殊情况也被化简了。     

GI／G／1排队系统的队长和等待时间的瞬时分布

本是[1，2]的继续,在本中利用马氏骨架过程给出了GI／G／1排队系统的队长的瞬时分布的另一新的计算方法和等待时间的计算方法。     

具有N—策略休假的M／G／1排除的同分解与最优策略

本文利用向量Ｍａｒｋｏｖ过程方法，研究了具有Ｎ－策略休假且休假时间为一般分布的Ｍ／Ｇ／１排队。它的两种特殊情况分别是具有多重休假的Ｍ／Ｇ／１排队和具有Ｎ－策略控制的Ｍ／Ｇ／１排队。     

M／G／1排队系统的队长几何遍历的新证法

证明了M／G／1排队系统中(L(f)，θ(t))几何遍历的充分必要条件是服务时间分布函数B(x)∈g^ (r)，改进了[2]的证明方法。     

M／M^r／1／N排队系统

本文讨论了等待空间有限的成批服务排队系统M/M~r/1/N,给出队长平稳分布的精确解.还得到了系统损失概率和平均输出间隔的精确值.     

同步休假GI／M／c排队的稳态理论

本文研究同步多重休假的GI／M／c排队系统,休假时间服从指数分布,使用发展了矩阵几何解决方法,给出了系统的平衡条件、稳态队长及等等时间分布。证明了队长和等等时间的条件随机分解定理,并讨论了由休假引起的附加队长和附加延迟的位相（PH）结构。     

异步休假M／M／C排队的稳态理论

本文研究异步休假的M／M／c排队,对多重休假和单重休假两类模型给出了统一的处理,得到了稳态队长,等等时间分布,提出了条件的随机分解的概念,证明服务台全忙条件下系统中排队顾客数和等待时间均可分解为两个独立随机变量之和,其中一个是经典无休假系统中对应的条件随机变量。     

Some results for the queues Mx/M/c and GIx/ G/c

We develop for the queue M^x/M/c an upper bound for the mean queue length and lower bounds for the delay probabilities (that of an arrival group and that of an arbitrary customer in the arrival group). An approximate formula is also developed for the general bulk-arrival queue GI^x/G/c. Preliminary numerical studies have indicated excellent performance of the results.     

关于环Fpm+uFpm+u2Fpm上循环码的注记

本文研究了环F_p^m+uF_p^m+u²F_p^m上长度为p^s的循环码分类.通过建立环F_p^m+uF_p^m+u²F_p^m到环F_p^m+uF_p^m的同态,给出了环F_p^m+uF_p^m+u²F_p^m上长度为p^s的循环码的新分类方法.应用这种方法,得到了环F_p^m+uF_p^m+u²F_p^m长度为p^s的循环码的码词数.     

Large-time asymptotics for the Gt/Mt/st+GIt many-server fluid queue with abandonment

We previously introduced and analyzed the G _t /M _t /s _t +GI _t many-server fluid queue with time-varying parameters, intended as an approximation for the corresponding stochastic queueing model when there are many servers and the system experiences periods of overload. In this paper, we establish an asymptotic loss of memory (ALOM) property for that fluid model, i.e., we show that there is asymptotic independence from the initial conditions as time t evolves, under regularity conditions. We show that the difference in the performance functions dissipates over time exponentially fast, again under the regularity conditions. We apply ALOM to show that the stationary G/M/s+GI fluid queue converges to steady state and the periodic G _t /M _t /s _t +GI _t fluid queue converges to a periodic steady state as time evolves, for all finite initial conditions.     

M/G/1/MLPS compared to M/G/1/PS

Multilevel processor sharing scheduling disciplines have recently been resurrected in papers that focus on the differentiation between short and long TCP flows in the Internet. We prove that, for M/G/1 queues, such disciplines are better than the processor sharing discipline with respect to the mean delay whenever the hazard rate of the service time distribution is decreasing.     

On the asymptotic behavior of xn+1=anxn/xn−1

We investigate the asymptotic behavior of solutions of a separable difference equation of the form

     

Une question sur les équations xm ? ym = Rzn (A Question on the Equations xm ? ym = Rzn)

Let m and n be integers at least two and R be a nonzero natural number. In this paper, we study the problem of the determination of the proper solutions of the Diophantine equation x ^m – y ^m equals; Rz ⁿ . We raise a question concerning the existence of any proper nontrivial solution of this equation, in case some precise conditions are satisfied by the triple (m, n, R). We prove some results about it.     

The least squares problem of the matrix equation A1X1B1^T ＋ A2X2B2^T = T

The matrix least squares （LS） problem minx ｜｜AXB^T--T｜｜F is trivial and its solution can be simply formulated in terms of the generalized inverse of A and B. Its generalized problem minx1,x2 ｜｜A1X1B1^T ＋ A2X2B2^T - T｜｜F can also be regarded as the constrained LS problem minx=diag（x1,x2） ｜｜AXB^T -T｜｜F with A = [A1, A2] and B = [B1, B2]. The authors transform T to T such that min x1,x2 ｜｜A1X1B1^T＋A2X2B2^T -T｜｜F is equivalent to min x=diag（x1 ,x2） ｜｜AXB^T - T｜｜F whose solutions are included in the solution set of unconstrained problem minx ｜｜AXB^T - T｜｜F. So the general solutions of min x1,x2 ｜｜A1X1B^T ＋ A2X2B2^T -T｜｜F are reconstructed by selecting the parameter matrix in that of minx ｜｜AXB^T - T｜｜F.     

Solving Ck/Cm/1/N queues by using characteristic roots in matrix analytic methods

In this paper, we study a C_k/C_m/1/N open queueing system with finite capacity. We investigate the property which shows that a product of the Laplace Stieltjes Transforms of interarrival and service times distributions satisfies an equation of a simple form. According to this equation, we present that the stationary probabilities on the unboundary states can be written as a linear combination of vector product-forms. Each component of these products is expressed in terms of roots of an associated characteristic polynomial. As a result, we carry out an algorithm for solving stationary probabilities in C_k/C_m/1/N systems, which is independent of N, hence greatly reducing the computational complexity.