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.     

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.     

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

     

Ueber das volle Formensystem der tern?ren biquadratischen Formf=x13x2+x23x3+x33x1

Ohne ZusammenfassungHieizu cme Tale     

Expansion in SLd(Z/qZ), q arbitrary

Let S be a fixed finite symmetric subset of SL _d (Z), and assume that it generates a Zariski-dense subgroup G. We show that the Cayley graphs of π _q (G) with respect to the generating set π _q (S) form a family of expanders, where π _q is the projection map Z→Z/q Z.     

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.