Queueing systems and networks with negative customers have been a subject of extensive research for two decades providing means to describe work-removal phenomena in different communication and information processing systems. This paper is the continuation of research devoted to elaboration of mathematical techniques for performance evaluation of queueing systems with different types of negativ...

This paper introduces and analyzes the notion of throughput suboptimality for many-server queueing systems in heavy traffic. The queueing model under consideration has multiple customer classes, indexed by a finite set I, and heterogenous, exponential servers. Servers are dynamically chosen to serve customers, and buffers are available for customers waiting to be served. The arrival rates and t...

This paper analyses two different queuing model (Model I and Model II) both consisting of three units connected in series separated by a buffer of finite capacity with finite number of parallel servers in each unit. Queuing model differs only on the provision of availing vacation to the servers in unit III. In Model I server can avail exponential vacation, whereas in Model II the server takes o...

An instance of the sorting buffer problem consists of a metric space and a server, equipped with a finite-capacity buffer capable of holding a limited number of requests. An additional ingredient of the input is an online sequence of requests, each of which is characterized by a destination in the given metric; whenever a request arrives, it must be stored in the sorting buffer. At any point in...

In this work, we revisit the theory underlying a range of time-dependent priority disciplines, and extend it to include the requirements of a class of applications that has not been studied in the past. Specifically, we target applications and services in which a scarce resource, or a fraction thereof, has to be awarded to a large number of concurrent requests. We thus consider an heavy traffic...

In Network-on-Chip (NoC), Time-Division-Mutiplexing(TDM) Virtual Circuit (VC) is well recognized as being capable to provide guaranteed services in both latency and bandwidth. We propose a method of modeling TDM based VC by using Network Calculus. We derive a tight upper bound of end-to-end delay and buffer requirement for indivdual VC. The performance analysis using Latency-Rate server is also...

In this paper, we studied single-server models of queuing-inventory systems (QIS) with catastrophes in the warehouse part and negative customers (n-customers) service facility. Consumer (c-customers) that arrived to buy inventory can be queued an infinite buffer. Under catastrophes, all system is destroyed but (on server or buffer) are still waiting for replenishment stocks. Upon arrival n-cust...