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An infinite-server queueing model with state-dependent arrival process and exponential distribution of service time is analyzed. It is assumed that the difference between the value of the arrival rate and total service rate becomes positive starting from a certain value of the number of customers in the system. In this paper, time until reaching this value by the number of customers in the system is called the pseudo steady-state period ( P S S P ). Distribution of duration of P S S P , its raw moments and its simple approximation under a certain scaling of the number of customers in the system are analyzed. Novelty of the considered problem consists of an arbitrary dependence of the rate of customer arrival on the current number of customers in the system and analysis of time until reaching from below a certain level by the number of customers in the system. The relevant existing papers focus on the analysis of time interval since exceeding a certain level until the number of customers goes down to this level (congestion period). Our main contribution consists of the derivation of a simple approximation of the considered time distribution by the exponential distribution. Numerical examples are presented, which confirm good quality of the proposed approximation. [ABSTRACT FROM AUTHOR]

An infinite-server queueing model with state-dependent arrival process and exponential distribution of service time is analyzed. It is assumed that the difference between the value of the arrival rate and total service rate becomes positive starting from a certain value of the number of customers in the system. In this paper, time until reaching this value by the number of customers in the system is called the pseudo steady-state period (PSSP). Distribution of duration of PSSP, its raw moments and its simple approximation under a certain scaling of the number of customers in the system are analyzed. Novelty of the considered problem consists of an arbitrary dependence of the rate of customer arrival on the current number of customers in the system and analysis of time until reaching from below a certain level by the number of customers in the system. The relevant existing papers focus on the analysis of time interval since exceeding a certain level until the number of customers goes down to this level (congestion period). Our main contribution consists of the derivation of a simple approximation of the considered time distribution by the exponential distribution. Numerical examples are presented, which confirm good quality of the proposed approximation.

Abstract: Temporal information processing, for instance the temporal association, plays an important role on many functions of brain. Among the various dynamics of neural networks, dynamic depression synapses and chaotic behavior have been regarded as the intriguing characteristics of biological neurons. In this paper, temporal association based on dynamic synapses and chaotic neurons is proposed. Interestingly, by introducing dynamic synapses into a temporal association, we found that the sequence storage capacity can be enlarged, that the transition time between patterns in the sequence can be shortened, and that the stability of the sequence can be enhanced. For particular interest, owing to chaotic neurons, the steady-state period becomes shorter in the temporal association and it can be adjusted by changing the parameter values of chaotic neurons. Simulation results demonstrating the performance of the temporal association are presented. [Copyright &y& Elsevier]

Sequential information processing, for instance the sequence memory, plays an important role on many functions of brain. In this paper, multi-sequence memory with controllable steady-state period and high sequence storage capacity is proposed. By introducing a novel exponential kernel sampling function and the sampling interval parameter, the steady-state period can be controlled, and the steady-state time steps are equal to the sampling interval parameter. Furthermore, we explained this phenomenon theoretically. Ascribing to the nonlinear function constitution for local field, the conventional Hebbian learning rule with linear outer product method can be improved. Simulation results show that neural network with nonlinear function constitution can effectively increase sequence storage capacity. [ABSTRACT FROM AUTHOR]

Abstract: A novel sparsely-connected neural network for sequence memory with controllable steady-state period is proposed in this study. By introducing a new exponential kernel sampling function and the sampling interval parameter, the steady-state period can be controlled, and the steady-state time steps is equal to the sampling interval parameter. Ascribing to the exponential kernel sampling function, the sequence storage capacity is enlarged compared with the existing sequence memory models. Owning to the sparsely-connected of Gaussian distribution, the model produces the efficient use of synapse resources, but the sequence storage capacity is decreased compared with the fully-connected networks. The study also gives a significant result that the networks of different dimensions have the same synapse connection efficiency if they are with the same connection mean degree. [Copyright &y& Elsevier]