We consider a bulk service G I / M / l queue with service rates depending on service batch size. If there are n customers waiting at the completion of service, min(n, I\) customers enter service. We show that the queue size and the service batch size at points of arrivals form an embedded Markov chain and the steady-state probabilities of this Markov chain have the matrix geometric form. We des...

We give improved deterministic algorithms for permutation routing and sorting on meshes with row and column buses. Among our results, we obtain a fairly simple algorithm for permutation routing on two-dimensional meshes with buses that achieves a running time of n + o(n) and a queue size of 2. We also describe an algorithm for routing on r-dimensional networks with a running time of (2? 1=r)n+ ...

In this paper, we present a randomized algorithm for the multipacket (i.e., k k) routing problem on an n x n mesh. The algorithm competes with high probability in at most kn + O(k log n) parallel communication steps, with a constant queue size of O(k). The previous best known algorithm [4] takes [5/4] kn + O([kn/f(n)]) steps with a queue size of O(k f(n)) (for any 1 ≤ f (n) ≤ n). We will also p...

Fast Congestion Notification (FN) one of the proactive queue management mechanisms that practices congestion avoidance to help avoid the beginning of congestion by marking/dropping packets before the router’s queue gets full; and exercises congestion control, when congestion avoidance fails, by increasing the rate of packet marking/dropping. Upon arrival of each packet, FN uses the instantaneou...

We look for protocols (service disciplines) setting an upper bound on the slowdown (expected sojourn time divided by job size) a job may face, irrespective of the processing times of other jobs. We call this worst slowdown the liability of a job. In a scheduling problem with identical release dates, allowing the server to randomize the order of service cuts almost in half the liability profiles...

This paper presents two algorithms to analytically approximate work in process (WIP)-dependent inter-departure times for tandem queues composed of a series of M/M/1 systems. The first algorithm is used for homogeneous tandem queues, the second for such with bottlenecks. Both algorithms are based on the possible combinations of distributing the WIP on the queues. For each combination the time to...

This paper presents a sensitivity investigation of the expected busy period for a controllable M/G/1 queueing system by means of a factorial design statistical analysis. We studies the effect of four important factors (parameters) that influence the expected busy period of an M/G/1 system, in which the server operates -policy in his idle period. A 2 4 factorial experimental design is used ...

We provide the first analytical expressions for expected waiting time of high-priority customers in delayed APQ by exploiting a classical conservation law work-conserving queues. Additionally, we describe an algorithm to compute times both low-priority and customers, which requires only truncation sums that converge quickly our experiments. These insights are used demonstrate how accumulation r...

In this paper we consider M[X]/G(a, b)/1 queueing system with accessible service, server breakdown without interruption, multiple vacation and closedown time. The service rule is as follows: the server starts service only when a minimum number of customers ′a′ is available in the queue and the maximum service capacity is ′b′ units such that late entries are allowed to join a service batch, with...

This study considers a -policy Geo/G/1 queue with startup and closedown times. The -policy operates as follows. On completion of the vacation, if there are customers in the queue, the server is either to activate with probability p or to stay dormant in the system with probability 1-p for waiting a new arrival; and if no customer presents in the queue, the server obeys classical sin...