On queueing systems with renewal departure processes

1983 ◽  
Vol 15 (03) ◽  
pp. 657-673 ◽  
Author(s):  
Mark Berman ◽  
Mark Westcott
Keyword(s):  
Queueing Systems ◽  
Sufficient Conditions ◽  
Arrival Process ◽  
Necessary Condition ◽  
Size Distributions ◽  
Departure Process ◽  
Arrival Processes ◽  
Departure Processes ◽  
Interval Distribution

It is proved that, for a large class of stable stationary queueing systems with renewal arrival processes and without losses, a necessary condition for the departure process also to be a renewal process is that its interval distribution be the same as that of the arrival process. This result is then applied to the classicalGI/G/squeueing systems. In particular, alternative proofs of known characterizations of theM/G/1 andGI/M/1 systems are given, as well as a characterization of theGI/G/∞ system. In the course of the proofs, sufficient conditions for the existence of all the moments of the stationary queue-size distributions of both theGI/G/1 andGI/G/∞ systems are derived.

On queueing systems with renewal departure processes

1983 ◽  
Vol 15 (3) ◽  
pp. 657-673 ◽  
Author(s):  
Mark Berman ◽  
Mark Westcott
Keyword(s):  
Queueing Systems ◽  
Sufficient Conditions ◽  
Arrival Process ◽  
Necessary Condition ◽  
Size Distributions ◽  
Departure Process ◽  
Arrival Processes ◽  
Departure Processes ◽  
Interval Distribution

It is proved that, for a large class of stable stationary queueing systems with renewal arrival processes and without losses, a necessary condition for the departure process also to be a renewal process is that its interval distribution be the same as that of the arrival process. This result is then applied to the classical GI/G/s queueing systems. In particular, alternative proofs of known characterizations of the M/G/1 and GI/M/1 systems are given, as well as a characterization of the GI/G/∞ system. In the course of the proofs, sufficient conditions for the existence of all the moments of the stationary queue-size distributions of both the GI/G/1 and GI/G/∞ systems are derived.

Stationary Poisson departure processes from non-stationary queues

1986 ◽  
Vol 23 (1) ◽  
pp. 256-260 ◽  
Author(s):  
Robert D. Foley
Keyword(s):  
Poisson Process ◽  
Service Time ◽  
Queueing Systems ◽  
Arrival Rate ◽  
Distribution Functions ◽  
Arrival Process ◽  
Service Time Distribution ◽  
Departure Process ◽  
Infinite Server ◽  
Departure Processes

We present some non-stationary infinite-server queueing systems with stationary Poisson departure processes. In Foley (1982), it was shown that the departure process from the Mt/Gt/∞ queue was a Poisson process, possibly non-stationary. The Mt/Gt/∞ queue is an infinite-server queue with a stationary or non-stationary Poisson arrival process and a general server in which the service time of a customer may depend upon the customer's arrival time. Mirasol (1963) pointed out that the departure process from the M/G/∞ queue is a stationary Poisson process. The question arose whether there are any other Mt/Gt/∞ queueing systems with stationary Poisson departure processes. For example, if the arrival rate is periodic, is it possible to select the service-time distribution functions to fluctuate in order to compensate for the fluctuations of the arrival rate? In this situation and in more general situations, it is possible to select the server such that the system yields a stationary Poisson departure process.

Stationary Poisson departure processes from non-stationary queues

1986 ◽  
Vol 23 (01) ◽  
pp. 256-260 ◽  
Author(s):  
Robert D. Foley
Keyword(s):  
Poisson Process ◽  
Service Time ◽  
Queueing Systems ◽  
Arrival Rate ◽  
Distribution Functions ◽  
Arrival Process ◽  
Service Time Distribution ◽  
Departure Process ◽  
Infinite Server ◽  
Departure Processes

We present some non-stationary infinite-server queueing systems with stationary Poisson departure processes. In Foley (1982), it was shown that the departure process from the Mt/Gt/∞ queue was a Poisson process, possibly non-stationary. The Mt/Gt /∞ queue is an infinite-server queue with a stationary or non-stationary Poisson arrival process and a general server in which the service time of a customer may depend upon the customer's arrival time. Mirasol (1963) pointed out that the departure process from the M/G/∞ queue is a stationary Poisson process. The question arose whether there are any other Mt/Gt/∞ queueing systems with stationary Poisson departure processes. For example, if the arrival rate is periodic, is it possible to select the service-time distribution functions to fluctuate in order to compensate for the fluctuations of the arrival rate? In this situation and in more general situations, it is possible to select the server such that the system yields a stationary Poisson departure process.

Separability criteria based on the Bloch representation of density matrices

2007 ◽  
Vol 7 (7) ◽  
pp. 624-638
Author(s):  
J. de Vicente
Keyword(s):  
Sufficient Conditions ◽  
Quantum Systems ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Pure Product ◽  
Separability Problem ◽  
Arbitrary Dimensions ◽  
Necessary And Sufficient ◽  
Bloch Representation

We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which we derive a necessary condition and sufficient conditions for separability. For a certain class of states the necessary condition and a sufficient condition turn out to be equivalent, therefore yielding a necessary and sufficient condition. The proofs of the sufficient conditions are constructive, thus providing decompositions in pure product states for the states that satisfy them. We provide examples that show the ability of these conditions to detect entanglement. In particular, the necessary condition is proved to be strong enough to detect bound entangled states.

On the identification of Poisson arrivals in queues with coinciding time-stationary and customer-stationary state distributions

1983 ◽  
Vol 20 (04) ◽  
pp. 860-871 ◽  
Author(s):  
Dieter König ◽  
Masakiyo Miyazawa ◽  
Volker Schmidt
Keyword(s):  
Stationary State ◽  
Queueing Systems ◽  
Sufficient Conditions ◽  
Arrival Process ◽  
Loss Probabilities ◽  
Poisson Arrivals ◽  
Number Of Customers

For several queueing systems, sufficient conditions are given ensuring that from the coincidence of some time-stationary and customer-stationary characteristics of the number of customers in the system such as idle or loss probabilities it follows that the arrival process is Poisson.

scholarly journals Asymptotic results for multiplexing subexponential on-off processes

1999 ◽  
Vol 31 (02) ◽  
pp. 394-421 ◽  
Author(s):  
Predrag R. Jelenković ◽  
Aurel A. Lazar
Keyword(s):  
Queueing System ◽  
Random Variable ◽  
Mean Value ◽  
Activity Period ◽  
Arrival Process ◽  
Asymptotic Results ◽  
Fluid Queue ◽  
Arrival Processes ◽  
Image Position

Consider an aggregate arrival process A N obtained by multiplexing N on-off processes with exponential off periods of rate λ and subexponential on periods τon. As N goes to infinity, with λN → Λ, A N approaches an M/G/∞ type process. Both for finite and infinite N, we obtain the asymptotic characterization of the arrival process activity period. Using these results we investigate a fluid queue with the limiting M/G/∞ arrival process A t ∞ and capacity c. When on periods are regularly varying (with non-integer exponent), we derive a precise asymptotic behavior of the queue length random variable Q t P observed at the beginning of the arrival process activity periods where ρ = 𝔼A t ∞ < c; r (c ≤ r) is the rate at which the fluid is arriving during an on period. The asymptotic (time average) queue distribution lower bound is obtained under more general assumptions regarding on periods than regular variation. In addition, we analyse a queueing system in which one on-off process, whose on period belongs to a subclass of subexponential distributions, is multiplexed with independent exponential processes with aggregate expected rate 𝔼e t . This system is shown to be asymptotically equivalent to the same queueing system with the exponential arrival processes being replaced by their total mean value 𝔼e t .

Bowl Shapes Are Better with Buffers–Sometimes

1991 ◽  
Vol 5 (2) ◽  
pp. 159-169 ◽  
Author(s):  
Jie Ding ◽  
Betsy S. Greenberg
Keyword(s):  
Buffer Capacity ◽  
Queueing System ◽  
Queueing Systems ◽  
Arrival Process ◽  
Departure Process ◽  
Optimal Arrangement ◽  
Service Distribution

We consider tandem queueing systems with a general arrival process and exponential service distribution. The queueing system consists of several stations with finite intermediate buffer capacity between the stations. We address the problem of determining the optimal arrangement for the stations. We find that considering the last two stations, the departure process is stochastically faster if the slower station is last. Our results are consistent with the “bowl shape” phenomenon that has been observed in serial queueing systems with zero buffer capacity.

On ∗-clean group rings over abelian groups

2016 ◽  
Vol 16 (08) ◽  
pp. 1750152 ◽  
Author(s):  
Dongchun Han ◽  
Yuan Ren ◽  
Hanbin Zhang
Keyword(s):  
Cyclic Group ◽  
Prime Power ◽  
Associative Ring ◽  
Finite Abelian Group ◽  
Sufficient Conditions ◽  
Complete Characterization ◽  
Necessary Condition ◽  
Group Rings ◽  
Prime Power Order

An associative ring with unity is called clean if each of its elements is the sum of an idempotent and a unit. A clean ring with involution ∗ is called ∗-clean if each of its elements is the sum of a unit and a projection (∗-invariant idempotent). In a recent paper, Huang, Li and Yuan provided a complete characterization that when a group ring [Formula: see text] is ∗-clean, where [Formula: see text] is a finite field and [Formula: see text] is a cyclic group of an odd prime power order [Formula: see text]. They also provided a necessary condition and a few sufficient conditions for [Formula: see text] to be ∗-clean, where [Formula: see text] is a cyclic group of order [Formula: see text]. In this paper, we extend the above result of Huang, Li and Yuan from [Formula: see text] to [Formula: see text] and provide a characterization of ∗-clean group rings [Formula: see text], where [Formula: see text] is a finite abelian group and [Formula: see text] is a field with characteristic not dividing the exponent of [Formula: see text].

scholarly journals An Interplay between Gabor and Wilson Frames

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
S. K. Kaushik ◽  
Suman Panwar
Keyword(s):  
Sufficient Conditions ◽  
Necessary Condition ◽  
Zak Transform ◽  
Bessel Sequence ◽  
Window Functions

Wilson frames{ψjk:w0,w-1∈L2(ℝ)}j∈ℤ,k∈ℕ0as a generalization of Wilson bases have been defined and studied. We give necessary condition for a Wilson system to be a Wilson frame. Also, sufficient conditions for a Wilson system to be a Wilson Bessel sequence are obtained. Under the assumption that the window functionsw0andw-1for odd and even indices ofjare the same, we obtain sufficient conditions for a Wilson system to be a Wilson frame (Wilson Bessel sequence). Finally, under the same conditions, a characterization of Wilson frame in terms of Zak transform is given.

scholarly journals Asymptotic results for multiplexing subexponential on-off processes

1999 ◽  
Vol 31 (2) ◽  
pp. 394-421 ◽  
Author(s):  
Predrag R. Jelenković ◽  
Aurel A. Lazar
Keyword(s):  
Queueing System ◽  
Random Variable ◽  
Mean Value ◽  
Activity Period ◽  
Arrival Process ◽  
Asymptotic Results ◽  
Fluid Queue ◽  
Arrival Processes ◽  
Image Position

Consider an aggregate arrival process AN obtained by multiplexing N on-off processes with exponential off periods of rate λ and subexponential on periods τon. As N goes to infinity, with λN → Λ, AN approaches an M/G/∞ type process. Both for finite and infinite N, we obtain the asymptotic characterization of the arrival process activity period.Using these results we investigate a fluid queue with the limiting M/G/∞ arrival process At∞ and capacity c. When on periods are regularly varying (with non-integer exponent), we derive a precise asymptotic behavior of the queue length random variable QtP observed at the beginning of the arrival process activity periods where ρ = 𝔼At∞ < c; r (c ≤ r) is the rate at which the fluid is arriving during an on period. The asymptotic (time average) queue distribution lower bound is obtained under more general assumptions regarding on periods than regular variation.In addition, we analyse a queueing system in which one on-off process, whose on period belongs to a subclass of subexponential distributions, is multiplexed with independent exponential processes with aggregate expected rate 𝔼et. This system is shown to be asymptotically equivalent to the same queueing system with the exponential arrival processes being replaced by their total mean value 𝔼et.

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