This paper considers a batch service polling system. We first study the case in which the server visits the queues cyclically, considering three different service regimes: gated, exhaustive, and globally gated. We subsequently analyze the case (the so called ‘Israeli Queue’) in which the server first visits the queue with the ‘oldest’ customer. In both cases, queue lengths and waiting times are...

1 The M/G/1 Queue Recall that an M/G/1 queue consists of a single server who receives customers at the times of a Poisson process at rate λ > 0 that wait in line to be served on a sequential basis in order of arrival. The i-th customer comes with a workload for the server given by the random variable ξi. The quantities {ξi : i ≥ 1} are i.i.d. The server processes incoming work at a constant (un...

An M/M/1 queueing system with second optional service and unreliable server is studied. We consider that the server works at different rate rather than being idle during the vacation period. The customers arrive to the system according to Poisson process with state dependent rates depending upon the server’s status. All customers demand the first essential service whereas only some of them dema...

In this article, the authors introduce a simple approach for modeling and analyzing a SII G / / 1 queue where the server may take repeated vacations. When a busy period ends, the server takes a vacation of random duration. At the end of each vacation, the server may either start a new vacation or resume service. If a queue is found of less than n customers, the server will always take a new vac...

Image inference using deep learning (DL) has recently become popular in a variety of applications. In the near future, real-time for delay sensitive images will be widespread with edge computing paradigm, where DL processing executed at network. this study, method future is proposed to infer large number images, which are aggregated from various end devices toward an server and temporarily stor...

We consider single-server and multi-server queues with deterministic reneging times motivated by the timeout mechanisms used in application servers.. A Volterra integral equation is developed using the level crossing analysis for the M/G/1 queue with reneging. An analytical solution is given for the M/HyperExponential/1 queue with deterministic reneging times and a numerical approach is present...

We present a heavy traffic analysis for a single server queue with renewal arrivals and generally distributed i.i.d. service times, in which the server employs the Shortest Remaining Processing Time (SRPT) policy. Under typical heavy traffic assumptions, we prove a diffusion limit theorem for a measure-valued state descriptor, from which we conclude a similar theorem for the queue length proces...

In this paper, we consider a two server system serving heterogeneous customers. One of the server has a FIFO scheduling policy and charges a fixed admission price to each customer. The second queue follows the highest-bidder-first (HBF) policy where an arriving customer bids for its position in the queue. Customers make an individually optimal choice of the server and for such system, we charac...

We propose a new queueing model named the acquisition queue. It differs from conventional queueing models in that the server not only serves customers, but also performs acquisition of new customers. The server has to divide its energy between both activities. The number of newly acquired customers is uncertain, and the effect of the server’s acquisition efforts can only be seen after some fixe...

This paper presents a discrete-time single-server finite buffer N threshold policy queue with renewal input and discrete Markovian service process. The server terminates service whenever the system becomes empty, and recommences service as soon as the number of waiting customers in the queue is N . We obtain the system-length distributions at prearrival and arbitrary epochs using the supplement...