Passage times for overtake-free paths in Gordon–Newell networks

Daduna, Hans

doi:10.1017/s000186780002070x

Cited by 23 publications

(23 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These are characterised by a unique root node and unique paths to a set of leaf nodes from each of which departures proceed to the root. Hence the term "tree-like", an instance of overtake-free [13,8] networks. The response time density function in this type of network can be found analytically, while the networks can be complex and the number of states in the underlying Markov chain can be made arbitrarily large by increasing the number of nodes or the customer population.…”

Section: Cycle Times In Queueing Networkmentioning

confidence: 99%

Passage time distributions in large Markov chains

Harrison

Knottenbelt

2002

SIGMETRICS Perform. Eval. Rev.

View full text Add to dashboard Cite

Probability distributions of response times are important in the design and analysis of transaction processing systems and computercommunication systems. We present a general technique for deriving such distributions from high-level modelling formalisms whose state spaces can be mapped onto finite Markov chains. We use a load-balanced, distributed implementation to find the Laplace transform of the first passage time density and its derivatives at arbitrary values of the transform parameter ¢. Setting ¢ ¤ £ ¦ ¥ yields moments while the full passage time distribution is obtained using a novel distributed Laplace transform inverter based on the Laguerre method. We validate our method against a variety of simple densities, cycle time densities in certain overtake-free (tree-like) queueing networks and a simulated Petri net model. Our implementation is thereby rigorously validated and has already been applied to substantial Markov chains with over 1 million states. Corresponding theoretical results for semi-Markov chains are also presented.

show abstract

Section: Cycle Times In Queueing Networkmentioning

confidence: 99%

Passage time distributions in large Markov chains

Harrison

Knottenbelt

2002

SIGMETRICS Perform. Eval. Rev.

View full text Add to dashboard Cite

show abstract

“…There seems to be no reason why the same induction argument and reversibility argument cannot be applied to the closed network model with nonovertaking paths as studied in [5], thus leading to an immediate extension of the theorem of the previous section. We shall not go into further details here.…”

Section: Extensionsmentioning

confidence: 99%

The Product Form for Sojourn Time Distributions in Cyclic Exponential Queues

Boxma

Kelly

Konheim

1984

J. ACM

View full text Add to dashboard Cite

show abstract

“…(The nonrepeating and nonovertaking properties are identical. The former term is used in [34], while the latter is well established in the literature on network of queues [9,14,351.) That is, it is possible for two packets to use a common link at stage il, different links at stage iz and a common link at stage is, for some il, iz, i3 where 1 5 i, < i2 < i3.…”

Section: Trafic Analysis: the Nonrenewal Casementioning

confidence: 99%

Randomized parallel communications on an extension of the omega network

Mitra

Cieślak

1987

J. ACM

View full text Add to dashboard Cite

Parallel communication algorithms and networks are central to large-scale parallel computing and, also, data communications. This paper identifies adverse source-destination traffic patterns and proposes a scheme for obtaining relief by means of randomized routing of packets on simple extensions of the well-known omega networks. Valiant and Aleliunas have demonstrated randomized algorithms, for a certain context which we call nonrenewal, that complete the communication task in time O(logN) with overwhelming probability, where N is the number of sources and destinations. Our scheme has advantages because it uses switches of fixed degree, requires no scheduling, and, for the nonrenewal context, is as good in proven performance. The main advantage of our scheme comes when we consider the renewal context in which packets are generated at the sources continually and asynchronously. Our algorithm extends naturally from the nonrenewal context. In the analysis in the renewal context we, first, explicitly identify the maximum traffic intensities in the internal links of the extended omega networks over all source-destination traffic specifications that satisfy loose bounds. Second, the benefits of randomization on the stability of the network are identified. Third, exact results, for certain restricted models for sources and transmission, and approximate analytic results, for quite general models, are derived for the mean delays. These results show that, in the stable regime, the maximum mean time from source to destination is asymptotically proportional to 1ogN. Numerical results are presented.

show abstract

Passage times for overtake-free paths in Gordon–Newell networks

Cited by 23 publications

References 4 publications

Passage time distributions in large Markov chains

Passage time distributions in large Markov chains

The Product Form for Sojourn Time Distributions in Cyclic Exponential Queues

Randomized parallel communications on an extension of the omega network

Contact Info

Product

Resources

About