Hardware Modules for Packet Interarrival Time Monitoring for Software Defined Measurements

2016 ◽  
Author(s):  
Racyus Pacifico ◽  
Pablo Goulart ◽  
Alex B. Vieira ◽  
Marcos A.M. Vieira ◽  
Jose Augusto M. Nacif
Keyword(s):  
Interarrival Time

On a Markovian queue with weakly correlated interarrival times

1981 ◽  
Vol 18 (01) ◽  
pp. 190-203 ◽  
Author(s):  
Guy Latouche
Keyword(s):  
Time Distribution ◽  
Queueing System ◽  
Interarrival Time ◽  
Probability Vector ◽  
Common Value ◽  
Markovian Queue ◽  
The Stability ◽  
Number Of Customers ◽  
Stationary Probabilities ◽  
Stationary Probability Vector

A queueing system with exponential service and correlated arrivals is analysed. Each interarrival time is exponentially distributed. The parameter of the interarrival time distribution depends on the parameter for the preceding arrival, according to a Markov chain. The parameters of the interarrival time distributions are chosen to be equal to a common value plus a factor ofε, where ε is a small number. Successive arrivals are then weakly correlated. The stability condition is found and it is shown that the system has a stationary probability vector of matrix-geometric form. Furthermore, it is shown that the stationary probabilities for the number of customers in the system, are analytic functions ofε, for sufficiently smallε, and depend more on the variability in the interarrival time distribution, than on the correlations.

SET-VALUED PERFORMANCE APPROXIMATIONS FOR THE QUEUE GIVEN PARTIAL INFORMATION

2020 ◽  
pp. 1-23
Author(s):  
Yan Chen ◽  
Ward Whitt
Keyword(s):  
Steady State ◽  
Decay Rate ◽  
Waiting Time ◽  
Partial Information ◽  
Upper And Lower Bounds ◽  
Interarrival Time ◽  
Limited Information ◽  
Wide Range ◽  
The Mean ◽  
Third Moment

In order to understand queueing performance given only partial information about the model, we propose determining intervals of likely values of performance measures given that limited information. We illustrate this approach for the mean steady-state waiting time in the $GI/GI/K$ queue. We start by specifying the first two moments of the interarrival-time and service-time distributions, and then consider additional information about these underlying distributions, in particular, a third moment and a Laplace transform value. As a theoretical basis, we apply extremal models yielding tight upper and lower bounds on the asymptotic decay rate of the steady-state waiting-time tail probability. We illustrate by constructing the theoretically justified intervals of values for the decay rate and the associated heuristically determined interval of values for the mean waiting times. Without extra information, the extremal models involve two-point distributions, which yield a wide range for the mean. Adding constraints on the third moment and a transform value produces three-point extremal distributions, which significantly reduce the range, producing practical levels of accuracy.

Embedded renewal processes in the GI/G/s queue

1972 ◽  
Vol 9 (3) ◽  
pp. 650-658 ◽  
Author(s):  
Ward Whitt
Keyword(s):  
Limit Theorems ◽  
Sufficient Conditions ◽  
Interarrival Time ◽  
Renewal Processes ◽  
Positive Probability ◽  
Functional Limit ◽  
Light Traffic ◽  
Functional Limit Theorems ◽  
Cumulative Processes ◽  
Rule Out

The stable GI/G/s queue (ρ < 1) is sometimes studied using the “fact” that epochs just prior to an arrival when all servers are idle constitute an embedded persistent renewal process. This is true for the GI/G/1 queue, but a simple GI/G/2 example is given here with all interarrival time and service time moments finite and ρ < 1 in which, not only does the system fail to be empty ever with some positive probability, but it is never empty. Sufficient conditions are then given to rule out such examples. Implications of embedded persistent renewal processes in the GI/G/1 and GI/G/s queues are discussed. For example, functional limit theorems for time-average or cumulative processes associated with a large class of GI/G/s queues in light traffic are implied.

The dependence of sojourn times on service times in tandem queues

1984 ◽  
Vol 21 (3) ◽  
pp. 661-667 ◽  
Author(s):  
Xi-Ren Cao
Keyword(s):  
Sojourn Time ◽  
Past History ◽  
Interarrival Time ◽  
Conditional Probabilities ◽  
Tandem Queues ◽  
Sojourn Times ◽  
Distributed Service ◽  
Service Times

In this paper we study a series of servers with exponentially distributed service times. We find that the sojourn time of a customer at any server depends on the customer's past history only through the customer's interarrival time to that server. A method of calculating the conditional probabilities of sojourn times is developed.

scholarly journals New Approach for Finding Basic Performance Measures of Single Server Queue

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Siew Khew Koh ◽  
Ah Hin Pooi ◽  
Yi Fei Tan
Keyword(s):  
Stationary State ◽  
Queue Length ◽  
Length Distribution ◽  
Cumulative Distribution ◽  
System Capacity ◽  
Interarrival Time ◽  
Single Server ◽  
Single Server Queue ◽  
Queue Length Distribution ◽  
Server Queue

Consider the single server queue in which the system capacity is infinite and the customers are served on a first come, first served basis. Suppose the probability density functionf(t)and the cumulative distribution functionF(t)of the interarrival time are such that the ratef(t)/1-F(t)tends to a constant ast→∞, and the rate computed from the distribution of the service time tends to another constant. When the queue is in a stationary state, we derive a set of equations for the probabilities of the queue length and the states of the arrival and service processes. Solving the equations, we obtain approximate results for the stationary probabilities which can be used to obtain the stationary queue length distribution and waiting time distribution of a customer who arrives when the queue is in the stationary state.

Tuxedo: Maximizing Smart Contract Computation in PoW Blockchains

2021 ◽  
Vol 5 (3) ◽  
pp. 1-30
Author(s):  
Sourav Das ◽  
Nitin Awathare ◽  
Ling Ren ◽  
Vinay J. Ribeiro ◽  
Umesh Bellur
Keyword(s):  
System Parameter ◽  
Security Analysis ◽  
Scaling Up ◽  
Interarrival Time ◽  
End To End Delay ◽  
Smart Contract ◽  
Key Innovation ◽  
Synchronous Network ◽  
And Performance ◽  
Harmful Effects

Proof-of-Work (PoW) based blockchains typically allocate only a tiny fraction (e.g., less than 1% for Ethereum) of the average interarrival time (I) between blocks for validating smart contracts present in transactions. In such systems, block validation and PoW mining are typically performed sequentially, the former by CPUs and the latter by ASICs. A trivial increase in validation time (τ) introduces the popularly known Verifier's Dilemma, and as we demonstrate, causes more forking and hurts fairness. Large τ also reduces the tolerance for safety against a Byzantine adversary. Solutions that offload validation to a set of non-chain nodes (a.k.a. off-chain approaches) suffer from trust and performance issues that are non-trivial to resolve. In this paper, we present Tuxedo, the first on-chain protocol to theoretically scale τ/I ≈1 in PoW blockchains. The key innovation in Tuxedo is to perform CPU-based block processing in parallel to ASIC mining. We achieve this by allowing miners to delay validation of transactions in a block by up to ζ blocks, where ζ is a system parameter. We perform security analysis of Tuxedo considering all possible adversarial strategies in a synchronous network with maximum end-to-end delay Δ and demonstrate that Tuxedo achieves security equivalent to known results for longest chain PoW Nakamoto consensus. Our prototype implementation of Tuxedo atop Ethereum demonstrates that it can scale τ without suffering the harmful effects of naive scaling up of τ/I in existing blockchains

Convexity results for single-server queues and for multiserver queues with constant service times

1990 ◽  
Vol 27 (02) ◽  
pp. 465-468 ◽  
Author(s):  
Arie Harel
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Sojourn Time ◽  
Interarrival Time ◽  
Service Rate ◽  
Single Server ◽  
Multiserver Queues ◽  
Service Rates ◽  
Constant Service Times ◽  
Number Of Customers

We show that the waiting time in queue and the sojourn time of every customer in the G/G/1 and G/D/c queue are jointly convex in mean interarrival time and mean service time, and also jointly convex in mean interarrival time and service rate. Counterexamples show that this need not be the case, for the GI/GI/c queue or for the D/GI/c queue, for c ≧ 2. Also, we show that the average number of customers in the M/D/c queue is jointly convex in arrival and service rates. These results are surprising in light of the negative result for the GI/GI/2 queue (Weber (1983)).

Assessment of Production Capacity and Ability of Rapid Response to Changing Customer Expectations

2015 ◽  
Vol 809-810 ◽  
pp. 1378-1383
Author(s):  
Iwona Paprocka ◽  
Sonia Cyba
Keyword(s):  
Production Systems ◽  
Production Capacity ◽  
Business Environment ◽  
Rapid Response ◽  
Interarrival Time ◽  
Company Size ◽  
Customer Expectations ◽  
New Concepts ◽  
A Company ◽  
Operating Company

Companies must respond quickly to customer needs and ensure the desired quality and low price in order to remain competitive in a market. It becomes necessary to create new concepts of production systems that meet all requirements imposed by consumers. The increase of reliability of machines and equipment, staff competence and forecasting a size and subject of demand increase the ability to react quickly to changes in the business environment. Therefore, the objective of this paper is to estimate the agility characteristics of a company (size of demand, interarrival time of orders and reliability of machines) and to verify its production capacity and rapid response capabilities. The characteristics are estimated for three variants of the production system: self-operating company, companies operating in cooperation, company buying additional machine.

State aggregation and discrete-state Markov chains embedded in a class of point processes

1995 ◽  
Vol 32 (01) ◽  
pp. 39-51
Author(s):  
Xi-Ren Cao
Keyword(s):  
Markov Chains ◽  
Poisson Process ◽  
Point Process ◽  
Point Processes ◽  
Marked Point ◽  
Practical Importance ◽  
Marked Point Process ◽  
Interarrival Time ◽  
Discrete State ◽  
State Aggregation

One result that is of both theoretical and practical importance regarding point processes is the method of thinning. The basic idea of this method is that under some conditions, there exists an embedded Poisson process in any point process such that all its arrival points form a sub-sequence of the Poisson process. We extend this result by showing that on the embedded Poisson process of a uni- or multi-variable marked point process in which interarrival time distributions may depend on the marks, one can define a Markov chain with a discrete state that characterizes the stage of the interarrival times. This implies that one can construct embedded Markov chains with countable state spaces for the state processes of many practical systems that can be modeled by such point processes.

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